Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary
x^2 – 3x – 12 = 0

A. –12.75, 15.75

B. 3.12, 3.77

C. 5.27, –2.27

D. 4.74, –1.74

Answer 1

$x^2- 3x - 12 = 0$

$x^2- 3x + ( \frac{3}{2} )^2 - ( \frac{3}{2} )^2 - 12 = 0$

$x^2- 3x + ( \frac{3}{2} )^2 - \frac{9}{4} - 12 = 0$

$x^2- 3x + ( \frac{3}{2} )^2 - \frac{57}{4} = 0$

$(x - \frac{3}{2} )^2 - \frac{57}{4} = 0$

$(x- \frac{3}{2} )^2 = \frac{57}{4}$

$(x - \frac{3}{2} ) = \pm \sqrt{ \frac{57}{4}}$

$x = \pm \sqrt{ \frac{57}{4}} + \frac{3}{2}$

$x = \ -2.27 \ or \ 5.27$ 

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Answer: x = 2.27 or + 5.27 (Answer C)
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