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Complete the square to solve the following quadratic equation: x6^2+2x-8=0

A. x=-10,x=8
B. x=-2,x=4
C. x=10,x=-8
D. x=2,x=-4

1 answer

To solve the quadratic equation \( x^2 + 2x - 8 = 0 \) by completing the square, we can follow these steps:

  1. Move the constant term to the other side of the equation: \[ x^2 + 2x = 8 \]

  2. Take half of the coefficient of \( x \), square it, and add it to both sides. The coefficient of \( x \) is 2, so half of it is 1, and squaring it gives us \( 1^2 = 1 \). \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

  3. Rewrite the left side as a squared term: \[ (x + 1)^2 = 9 \]

  4. Take the square root of both sides: \[ x + 1 = \pm 3 \]

  5. Solve for \( x \):

    • If \( x + 1 = 3 \): \[ x = 3 - 1 = 2 \]
    • If \( x + 1 = -3 \): \[ x = -3 - 1 = -4 \]

Thus, the solutions are \( x = 2 \) and \( x = -4 \).

The correct answer is: D. \( x = 2, x = -4 \)