Question

Solve by completing the square: x2-8x+7=0
That is an x squared.
Thanks.

Answer 1

Let's use \(x^2 - 4x - 8 = 0\) to demonstrate Completing the Square.
1. Put the constant term on the other side of the equation by adding 8 to both sides.
\(x^2 - 4x = 8\)
2. Look at the coefficient of the x-term (-4) -> take half this term (-2) and square it (+4). Add this to both sides.
\(x^2 - 4x + 4 = 12\) This is a perfect square and can be factored.
3. Factor:
\((x-2)^2\)
(hint: The constant term is the same as half of the x term that was squared in step 2.)
4. Solve for x:
\(\sqrt{(x-2)^2} = \sqrt{12}\)
\(x - 2 = \pm 2 \sqrt{3}\)
\(x = 2 \pm 2 \sqrt{3}\)

Please ask if anything is unclear.