The equation x^2 - 2x - 8 = 0 is solved by completing the square. The value of x is either 4 or - 2.
How to complete the square?
A square can be completed by adding and subtracting a number with the equation. It is done in such a way that makes the equation into a square.
The equation can be solved as shown below:
x^2 - 2x - 8 = 0
Add and subtract 1 from it:
x^2 - 2x + 1 -1 - 8 = 0
⇒ ( x -1 )^2 - 9 = 0
⇒ ( x - 1 )^2 = 9
The square root of this equation can be either:
x - 1 = 3
or x - 1 = -3
We can simplify both equations to get x = 4 and x = -2 respectively.
Therefore, the equation x^2 - 2x - 8 = 0 is solved by completing the square. The value of x is either 4 or - 2. The correct answer is option A.
Learn more about completing the square here: https://brainly.com/question/1596209
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