Solving Quadratic Equations by Completing the Squares

Which formula do you use to find the "c-value" that makes a quadratic a perfect square trinomial?

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CCSS.HSA-REI.B.4B

Solve the following quadratics equation by completing the square... x² + 4x - 1 = 0

• x = -2 ± √5

• x = -5 ± √2

• x = 2 ± √5

• x = -5 ± √5

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CCSS.HSA-REI.B.4B

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CCSS.HSA-REI.B.4B

• Divide by 2

• Subtract 8 from both sides

• Add 16 to both sides

• Move all terms to one side

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CCSS.HSA-REI.B.4B

• 6

• 36

• -6

• -36

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CCSS.HSA-REI.B.4B

• Add 30 to both sides

• Divide by 2

• Subtract 30 from both sides

• Multiply by 2

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CCSS.HSA-REI.B.4B

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CCSS.HSA-REI.B.4B

• 3

• 6

• -3

• -6

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CCSS.HSA-REI.B.4B

Reorder the following steps to solve a quadratic equation when the leading coefficient is 1 (a = 1) to solve the equation by completing the square.

• Take the square root of both sides and solve for both cases.

• Take half of b, square it, then

  add this to both sides.

• Factor the perfect square trinomial.

• Rewrite as

  x² + bx = c

• Write the answer using curly braces in set notation

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CCSS.HSA-REI.B.4B

What are the steps to solving this by completing the square?

• Subtract 5 from both sides of the equation

• Subtract 21 from both sides of the equation

• Take the square root of both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

Answer explanation

Steps for completing the square when a=1

1st: Rewrite as x² + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

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CCSS.HSA-REI.B.4B