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


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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.

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10.5 Solving Quadratic Equations By Completing the Square

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10 5 solving quadratic equations by completing the square

10.5 Solving Quadratic Equations By Completing the Square


Review square root method

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

Square Root Method

Be sure to give both the positive and negative answers!


Solving quadratic equations

Solving Quadratic Equations

by Completing the Square

Goal: Turn the problem into a Square Root Problem


Completing the square

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


Example 4 3a

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

Step 1Find one half of 16.

Step 2Square the result of Step 1.

Step 3Add the result of Step 2to

Answer:The trinomial can be written as

Example 4-3a


Example 4 3b

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

Example 4-3b

Answer: 9; (x + 3)2


Example 4 4a

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 4-4a


Example 4 4a1

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}.


Example 4 4b

Solve by completing the square.

Example 4-4b

Answer:{–6, 1}


Example 4 5a

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 4-5a


Example 4 5a1

Write the left side as a perfect square by factoring. Simplify the right side.

Square Root Property

Add to each side.

Example 4-5a


Example 4 5a2

Solve each equation.

Answer: The solution set is

Write as two equations.

or

Example 4-5a


Example 4 5b

Example 4-5b

Classwork/Homework


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