9.2.4 Making a Perfect Square

Algebra 19.2.4 Making a Perfect Square

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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?

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

$x^{2} + 12 x$

The constant term $c = 36$ can be added to make the perfect square $x^{2} + 12 x + 36$ .

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

$x^{2} - 6 x + 1$

8 can be added to the constant term $c = 1$ to make the perfect square $x^{2} - 6 x + 9$ .

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

$x^{2} + 14 x - 10$

59 can be added to the constant term $c = - 10$ to make the perfect square $x^{2} + 14 x + 49$ .

Solve the equation $x^{2} - 16 x = - 60$ by completing the square. Show your reasoning.

Compare your answer:

$x^{2} - 16 x = - 60 x^{2} - 16 x + 64 = - 60 + 64 x^{2} - 16 x + 64 = 4 (x - 8)^{2} = 4 \sqrt{(x - 8)^{2}} = \sqrt{4} x - 8 = \pm 2 x - 8 = 2 x - 8 = - 2 x = 6 or x = 10$

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