10.5 Solving Quadratic Equations By Completing the Square

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# 10.5 Solving Quadratic Equations By Completing the Square - PowerPoint PPT Presentation

10.5 Solving Quadratic Equations By Completing the Square. 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.

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### 10.5 Solving Quadratic Equations By Completing the Square

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

Solve by completing the square.

Notice that is not a perfect square.

Rewrite so the left side is of the form

Since

Write the left side as a perfect square by factoring.

Example 4-4a
Square Root Property

Subtract 2 from each side.

Write as two equations.

or

Solve each equation.

Example 4-4a

Answer: 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.

Since

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

Square Root Property

Example 4-5a
Solve each equation.