Question

2.

Answer 1

Answer:

C

Step-by-step explanation:

Given

x² - 3x - 12 = 0 ( add 12 to both sides )

x² - 3x = 12

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(-$\frac{3}{2}$ )x + $\frac{9}{4}$ = 12 + $\frac{9}{4}$

(x - $\frac{3}{2}$ )² = $\frac{57}{4}$ ( take the square root of both sides )

x - $\frac{3}{2}$ = ± $\sqrt{\frac{57}{4} }$ = ± $\frac{\sqrt{57} }{2}$ ( add $\frac{3}{2}$ to both sides )

x = $\frac{3}{2}$ ± $\frac{\sqrt{57} }{2}$

Then

x = $\frac{3}{2}$ + $\frac{\sqrt{57} }{2}$ ≈ 5.27 ( to the nearest hundredth )

x = $\frac{3}{2}$ - $\frac{\sqrt{57} }{2}$ ≈ - 2.27 ( to the nearest hundredth )