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 + ( (3)/(2) )^2 - ( (3)/(2) )^2 - 12 = 0`


`x^2- 3x + ( (3)/(2) )^2 - (9)/(4) - 12 = 0`


`x^2- 3x + ( (3)/(2) )^2 - (57)/(4) = 0`


`(x - (3)/(2) )^2 - (57)/(4) = 0`


`(x- (3)/(2) )^2 = (57)/(4)`


`(x - (3)/(2) ) = \pm \sqrt{ (57)/(4)}`


`x = \pm \sqrt{ (57)/(4)} + (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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