9.4.5 Perfect Square and Squared Factors

Algebra 19.4.5 Perfect Square and Squared Factors

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9.4.5 • Perfect Square and Squared Factors

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1. Answer the following questions for expression $4 x^{2} - 28 x + c$ .

a. Find the value of $c$ to make the expression a perfect square.

49. Standard form: $4 x^{2} - 28 x + 49$ .

b. Write an equivalent expression in the form of squared factors.

Compare your answer:

Squared factors: $(2 x - 7)^{2}$ .

2. Solve the equation $4 x^{2} - 28 x = - 33$ by completing the square. Show your reasoning.

Compare your answer:

$4 x^{2} - 28 x = - 33 4 x^{2} - 28 x + 49 = - 33 + 49 (2 x - 7)^{2} = 16 \sqrt{(2 x - 7)^{2}} = \sqrt{16} 2 x - 7 = 4 2 x - 7 = - 4 2 x = 11 2 x = 3$

$x = \frac{11}{2} and x = \frac{3}{2}$

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