Write your quadratic equation on a sheet of paper in the standard format of ax^2 + bx + c = 0. We can use x^2 + 6x -7 = 0 as an example.
Move the non-variable in the equation over to the right side of the equal sign. In this example, add seven to both sides of the equal sign to get x^2 + 6x = 7.
Divide the number attached to the x-variable by two and square it. Add the resulting square to both sides of the equation. In this example, divide six by two to get three. Multiply three times three to get nine. Add nine to both sides of the equal sign to get x^2 + 6x + 9 = 16.
Factor the equation on the left side of the equal sign. In this example, you should get (x + 3)^2 = 16.
Find the square root of both sides of the equal sign. Remember that positive numbers have two square roots, so you will get two resulting equations. In this example, you should get x + 3 = 4 and x + 3 = -4.
Solve for the x-variable in both equations. In the first equation, you should get x = 1. In the second equation, you should get x = -7. Minus-seven and one are your two solutions for the equation.