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10.5 Solving Quadratic Equations By Completing the SquarePowerPoint Presentation

10.5 Solving Quadratic Equations By Completing the Square

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### 10.5 Solving Quadratic Equations By Completing the Square

### Solving Quadratic Equations

Review Square Root Method

- Use if there is no linear term. (i.e. B = 0)
- Get the Quadratic Term on one side and the Constant on the other side.
- Simply take the Square Root of Both Sides.

Square Root Method

Be sure to give both the positive and negative answers!

by Completing the Square

Goal: Turn the problem into a Square Root Problem

Completing the Square

- Take HALF the coefficient of the linear term (i.e. B ) and square.
- Example: x2 + 8x + c
- Example: x2 + 12x + c
- Example: x2 + 9x + c

c = 16

c = 36

c = 81/4

Find the value of c that makes a perfect square. Then write the trinomial as a perfect square.

Step 1 Find one half of 16.

Step 2 Square the result of Step 1.

Step 3 Add the result of Step 2 to

Answer:The trinomial can be written as

Example 4-3aFind the value of c that makes a perfect square. Then write the trinomial as a perfect square.

Example 4-3bAnswer: 9; (x + 3)2

Solve by completing the square.

Notice that is not a perfect square.

Rewrite so the left side is of the form

Since

add 4 to each side.

Write the left side as a perfect square by factoring.

Example 4-4aSubtract 2 from each side.

Write as two equations.

or

Solve each equation.

Example 4-4aAnswer: The solution set is {–6, 2}.

Solve by completing the square.

Notice thatis not a perfect square.

Divide by the coefficient of the quadratic term, 3.

Add to each side.

Since

add to each side.

Example 4-5aWrite the left side as a perfect square by factoring. Simplify the right side.

Square Root Property

Add to each side.

Example 4-5aExample 4-5b

Classwork/Homework

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