4.6 completing the square
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4.6 COMPLETING THE SQUARE
SOLVING BY FINDING SQUARE ROOTS
Solving equations of the form1. Isolate the variable2. “Undo the Square” by taking the square root
of both sides
Don’t forget: when you take the square root your solution is ±
2ax c
EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
24 10 46x
EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
23 5 25x
EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
23 16 1x Note: No real number squared is equal to – 5, so the equation does not have a real number solution
SOLVING A PERFECT SQUARE TRINOMIAL Remember that a perfect square trinomials
are of the form:
Sometimes they can be set equal to a constant
2 2
2 2
2
2
a ab b
a ab b
SOLVING A PERFECT SQUARE TRINOMIAL
When a perfect square trinomial is set equal to a constant:
1. Factor the trinomial2. Take the square root of both sides3. Solve for the value of the variable
EXAMPLE: SOLVE EACH EQUATION
2 4 4 25x x
EXAMPLE: SOLVE EACH EQUATION
2 14 49 25x x
COMPLETING THE SQUARE
If is part of a perfect square trinomial, we can find a constant c so that
is a perfect square trinomial.
This is a process called completing the square
2x bx2x bx c
COMPLETING THE SQUARE
We can form a perfect square trinomial
from by adding 2x bx
2
2
b
COMPLETE THE SQUARE
1. Find the value of
2. Add the value to the expression, this completes the square
2
2
b
2x bx
EXAMPLE: COMPLETE THE SQUARE
2 6x x
EXAMPLE: COMPLETE THE SQUARE
2 10x x
SOLVING AN EQUATION BY COMPLETING THE SQUARE
1. Rewrite the equation so it is of the form
2. Complete the Square: Add to both sides
3. Factor the prefect square trinomial4. Take the square root of both sides5. Solve for the variable
2x bx c 2
2
b
EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
23 12 6 0x x
EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
22 3 9x x x
HOMEWORK
P 237 #1 – 8, 12 – 45 odd