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Making a Perfect Square

9.2.4 Making a Perfect Square

9.2.4 • Making a Perfect Square

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For questions 1 – 3, what could be added to each expression to make it a perfect square?

1.

What could be added to make the expression a perfect square?

x 2 + 12 x x 2 + 12 x

The constant term c=36c=36 can be added to make the perfect square x2+12x+36x2+12x+36.

2.

What could be added to make the expression a perfect square?

x 2 − 6 x + 1 x 2 − 6 x + 1

8 can be added to the constant term c=1c=1 to make the perfect square x2−6x+9x2−6x+9.

3.

What could be added to make the expression a perfect square?

x 2 + 14 x − 10 x 2 + 14 x − 10

59 can be added to the constant term c=−10c=−10 to make the perfect square x2+14x+49x2+14x+49.

4.

Solve the equation x2−16x=−60x2−16x=−60 by completing the square. Show your reasoning.

Compare your answer:

x2−16x=−60x2−16x+64=−60+64x2−16x+64=4(x−8)2=4(x−8)2=4x−8=±2x−8=2x−8=−2x=6 or x=10x2−16x=−60x2−16x+64=−60+64x2−16x+64=4(x−8)2=4(x−8)2=4x−8=±2x−8=2x−8=−2x=6 or x=10