Answer: the solutions to the quadratic equation 4x^2 + 8x - 2 = 0, found by completing the square, are x = -1 + √2 and x = -1 - √2.
Explanation:
To solve the quadratic equation 4x^2 + 8x - 2 = 0 by completing the square, we can follow these steps:
Divide both sides of the equation by 4 to get a coefficient of 1 for the x^2 term:
x^2 + 2x - 1/2 = 0
Move the constant term to the right-hand side of the equation:
x^2 + 2x = 1/2
Add and subtract the square of half the coefficient of the x term to the left-hand side of the equation. Half the coefficient of the x term is 1, so we need to add and subtract 1^2 = 1:
x^2 + 2x + 1 - 1 - 1/2 = 1/2
Group the perfect square trinomial on the left-hand side and simplify:
(x + 1)^2 - 3/2 = 1/2
Add 3/2 to both sides of the equation:
(x + 1)^2 = 2
Take the square root of both sides of the equation, remembering to include both the positive and negative square roots:
x + 1 = ±√2
Subtract 1 from both sides of the equation to isolate x:
x = -1 ± √2
Therefore, the solutions to the quadratic equation 4x^2 + 8x - 2 = 0, found by completing the square, are x = -1 + √2 and x = -1 - √2.