Download - Topic 4 solving quadratic equations part 2
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Solving Quadratic EquationsModule 10 - Topic 4
PART 2
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Solving Quadratic Equations when they do NOT equal ZERO
• So far all the quadratic equations we’ve solve have been equal to zero but not all are so nice. If they don’t equal zero, make them equal to zero!
• View this Cool Math website to how to solve Quadratic Equations when the original equation is not equal to 0.
• There are 3 pages to view.
• Complete the Your Turn problems in your notebook and check your answers on the next slide.
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
x + 3( ) x − 6( ) = 0
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
x + 3( ) x − 6( ) = 0x + 3 = 0 or x − 6 = 0
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
x + 3( ) x − 6( ) = 0x + 3 = 0 or x − 6 = 0
−3 −3 +6 +6
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
x + 3( ) x − 6( ) = 0x + 3 = 0 or x − 6 = 0
−3 −3 +6 +6
x = −3 or x = 6
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Page 1 - Finish it• Solve. x2 − 3x −18 = 0
x + 3( ) x − 6( ) = 0x + 3 = 0 or x − 6 = 0
−3 −3 +6 +6
x = −3 or x = 6
Answer: −3,6{ }
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Page 1 - Your Turn• Solve. x2 + 7x = 170
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Page 1 - Your Turn• Solve. x2 + 7x = 170
−170 −170
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Page 1 - Your Turn• Solve. x2 + 7x = 170
−170 −170
x2 + 7x −170 = 0
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Page 1 - Your Turn• Solve. x2 + 7x = 170
x +17( ) x −10( ) = 0
−170 −170
x2 + 7x −170 = 0
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Page 1 - Your Turn• Solve. x2 + 7x = 170
x +17( ) x −10( ) = 0x +17 = 0 or x −10 = 0
−170 −170
x2 + 7x −170 = 0
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Page 1 - Your Turn• Solve. x2 + 7x = 170
x +17( ) x −10( ) = 0x +17 = 0 or x −10 = 0−17 −17 +10 +10
−170 −170
x2 + 7x −170 = 0
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Page 1 - Your Turn• Solve. x2 + 7x = 170
x +17( ) x −10( ) = 0x +17 = 0 or x −10 = 0−17 −17 +10 +10
x = −17 or x = 10
−170 −170
x2 + 7x −170 = 0
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Page 1 - Your Turn• Solve. x2 + 7x = 170
x +17( ) x −10( ) = 0x +17 = 0 or x −10 = 0−17 −17 +10 +10
x = −17 or x = 10
−170 −170
x2 + 7x −170 = 0
Answer: −17,10{ }
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 0
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
−1 −1 +3 +3
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
−1 −1 +3 +3
2x = −1 or x = 3
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
−1 −1 +3 +3
2x = −1 or x = 3 2 2
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
−1 −1 +3 +3
x = − 12
2x = −1 or x = 3 2 2
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Page 2 - Finish it• Solve. 2x2 − 5x − 3 = 0
2x +1( ) x − 3( ) = 02x +1 = 0 or x − 3 = 0
−1 −1 +3 +3
x = − 12
2x = −1 or x = 3 2 2
Answer: −12
,3⎧⎨⎩
⎫⎬⎭
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 0
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−2 −2 +3 +3
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−2 −2 +3 +3
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
5x = −2 or 2x = 3
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−2 −2 +3 +3
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
5x = −2 or 2x = 3 5 5 2 2
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−2 −2 +3 +3
x = − 25 or x = 3
2
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
5x = −2 or 2x = 3 5 5 2 2
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Page 2 - Your Turn• Solve. 11x + 6 −10x2 = 0
5x + 2( ) 2x − 3( ) = 05x + 2 = 0 or 2x − 3 = 0
−2 −2 +3 +3
x = − 25 or x = 3
2
−11x − 6 +10x2 = 0
−1 11x + 6 −10x2( ) = 0 ⋅ −1
10x2 −11x − 6 = 0
5x = −2 or 2x = 3 5 5 2 2 Answer: −
25
, 32
⎧⎨⎩
⎫⎬⎭
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Page 3 - Your Turn• Solve. −16x = −4x3
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Page 3 - Your Turn• Solve. −16x = −4x3
+4x3 +4x3
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Page 3 - Your Turn• Solve. −16x = −4x3
4x3 −16x = 0+4x3 +4x3
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Page 3 - Your Turn• Solve. −16x = −4x3
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
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Page 3 - Your Turn• Solve. −16x = −4x3
4x x + 2( ) x − 2( ) = 0
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
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Page 3 - Your Turn• Solve. −16x = −4x3
4x x + 2( ) x − 2( ) = 0
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
4x = 0 or x + 2 = 0 or x − 2 = 0
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Page 3 - Your Turn• Solve. −16x = −4x3
4x x + 2( ) x − 2( ) = 0
4 4 −2 −2 +2 +2
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
4x = 0 or x + 2 = 0 or x − 2 = 0
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Page 3 - Your Turn• Solve. −16x = −4x3
4x x + 2( ) x − 2( ) = 0
4 4 −2 −2 +2 +2
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
4x = 0 or x + 2 = 0 or x − 2 = 0
x = 0 or x = −2 or x = 2
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Page 3 - Your Turn• Solve. −16x = −4x3
4x x + 2( ) x − 2( ) = 0
4 4 −2 −2 +2 +2
4x3 −16x = 0+4x3 +4x3
4x x2 − 4( ) = 0
4x = 0 or x + 2 = 0 or x − 2 = 0
x = 0 or x = −2 or x = 2
Answer: 0,−2,2{ }
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Do you want to Play a GAME?• Check your knowledge on solving Quadratic
Equations by playing Jeopardy. Ok, technically it’s called Challenge Board but it’s the same idea!
• You have the option to play alone or against a friend or maybe a family member!
• You could even arrange a time with a classmate to meet on Pronto to play. Try the App Share feature to see the same game board!
• Finding the x-intercepts is the same as solving!
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Fantastic Job!• You’ve finished reviewing Solving Quadratic
Equations Part 2.
• Exit and proceed to the Mastery Assignment.