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Solve the equation 2x^2+8x-1=o by completing the square. Give your answer to 2 decimal places

1 Answer

3 votes

Answer:

x ≈ - 4.12 , x ≈ 0.12

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 =
(9)/(2) ( take the square root of both sides )

x + 2 = ±
\sqrt{(9)/(2) } = ±
(3)/(√(2) ) = ±
(3√(2) )/(2) ( subtract 2 from both sides )

x = - 2 ± 1.5
√(2) , thus

x = - 2 - 1.5
√(2) ≈ - 4.12 ( to 2 dec. places )

x = - 2 + 1.5
√(2) ≈ 0.12 ( to 2 dec. places )

User Phatduckk
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