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(-[tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] = 12 + [tex]\frac{9}{4}[/tex]
(x - [tex]\frac{3}{2}[/tex] )² = [tex]\frac{57}{4}[/tex] ( take the square root of both sides )
x - [tex]\frac{3}{2}[/tex] = ± [tex]\sqrt{\frac{57}{4} }[/tex] = ± [tex]\frac{\sqrt{57} }{2}[/tex] ( add [tex]\frac{3}{2}[/tex] to both sides )
x = [tex]\frac{3}{2}[/tex] ± [tex]\frac{\sqrt{57} }{2}[/tex]
Then
x = [tex]\frac{3}{2}[/tex] + [tex]\frac{\sqrt{57} }{2}[/tex] ≈ 5.27 ( to the nearest hundredth )
x = [tex]\frac{3}{2}[/tex] - [tex]\frac{\sqrt{57} }{2}[/tex] ≈ - 2.27 ( to the nearest hundredth )
