8.3

Solving Equations by Using Quadratic

Methods

Solving Quadratic EquationsSolving a Quadratic Equation1. If the equation is in the form (ax + b)2 = c, use the

square root property to solve. If not, go to Step 2.2. Write the equation in standard form: ax2 + bx + c = 0.3. Try to solve the equation by the factoring method.

If not possible, go to Step 4.4. Solve the equation by the quadratic formula.

Solve the following equation.42 xx

Example

Solve the following equation.1

24

25

xx

Example

Solve: 9x4 + 5x2 – 4 = 0

Example

Continued

Solve: 3x2/3 + 11x1/3 = 4

Example

Continued

ExampleTogether, an experienced word processor and an apprentice word processor can create a document in 6 hours. Alone, the experienced word processor can process the document 2 hours fasters than the apprentice. Find the time in which each person can create the document alone.x = the time in hours it take the apprenticex – 2 = the time in hours it takes the experienced word processor Total Hours to

Complete JobPart of JobCompleted in 1 Hour

Apprentice

Experienced

Together

Example (cont)

Beach and Fargo are about 400 miles apart. A salesperson travels from Fargo to Beach one day at a certain speed. She returns to Fargo the next day and drives 10 mph faster. Her total time was hours. Find her speed to Beach and the return speed to Fargo.

2143

Example

Continued

Example (cont)