Answer:
x ≈ - 4.12 , x ≈ 0.12
Step-by-step explanation:
Given
2x² + 8x - 1 = 0 ( add 1 to both sides )
2x² + 8x = 1 ← factor out 2 on the left side
2(x² + 4x) = 1
To complete the square
add/ subtract (half the coefficient of the x- term )² to x² + 4x
2(x² + 2(2)x + 4 - 4) = 1, that is
2(x + 2)² - 8 = 1 ( add 8 to both sides )
2(x + 2)² = 9 ( divide both sides by 2 )
(x + 2)² = [tex]\frac{9}{2}[/tex] ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{\frac{9}{2} }[/tex] = ± [tex]\frac{3}{\sqrt{2} }[/tex] = ± [tex]\frac{3\sqrt{2} }{2}[/tex] ( subtract 2 from both sides )
x = - 2 ± 1.5[tex]\sqrt{2}[/tex] , thus
x = - 2 - 1.5[tex]\sqrt{2}[/tex] ≈ - 4.12 ( to 2 dec. places )
x = - 2 + 1.5[tex]\sqrt{2}[/tex] ≈ 0.12 ( to 2 dec. places )
