Find the solutions of the equation by completing the square.
x^2-6x=7_
x^2-6x_= 7_
(x-_)^2 =_
x-3=_
x-3=_ and x-3 =_
To complete the square for the equation x^2 - 6x = 7:
1. Move the constant term to the right side: x^2 - 6x = 7 becomes x^2 - 6x + _ = 7 + _.
2. In order to complete the square, calculate and add half of the coefficient of x squared (which is -6/2 = -3) squared to both sides:
x^2 - 6x + (-3)^2 = 7 + (-3)^2
x^2 - 6x + 9 = 7 + 9
x^2 - 6x + 9 = 16
3. Rewrite the left side as a squared binomial:
(x - 3)^2 = 16
4. Take the square root of both sides to solve for x:
x - 3 = ±√16
x - 3 = ±4
x = 3 ± 4
Therefore, the solutions are x = 3 + 4 = 7 and x = 3 - 4 = -1.