Answer:
x ≈ - 4.12 , x ≈ 0.12
Step-by-step explanation:
2x² + 8x - 1 = 0 ( add 1 to both sides )
2x² + 8x = 1 ( factor out 2 from the first two terms )
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
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 square root of both sides )
x + 2 = ± [tex]\sqrt{\frac{9}{2} }[/tex] = ± [tex]\frac{3}{\sqrt{2} }[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\frac{3}{\sqrt{2} }[/tex]
Then
x = - 2 - [tex]\frac{3}{\sqrt{2} }[/tex] ≈ - 4.12 ( to 2 dec. places )
x = - 2 + [tex]\frac{3}{\sqrt{2} }[/tex] ≈ 0.12 ( to 2 dec. places )
