Solve the quadratic equation by completing the square

x^2-12+7=0

Just to preface: quadratic equations take the form ax^2 + bx + c. (Did you mean x^2 - 12x + 7) ?

First, move the c term to the right side of the equation:

x^2 - 12x = - 7

Then, calculate (b/2) ^2:

(-12/2) ^2 = (-6) ^2 = 36

Now add 36 to both sides:

x^2 - 12x + 36 = 7 + 36

x^2 - 12x + 36 = 43

Now factor the left side:

(x + 6) ^2 = 43

And solve algebraically. sqrt = square root

sqrt (x + 6) ^2 = + / - sqrt43

x + 6 = + / - sqrt43

x = + / - sqrt43 - 6, or

x = - 6 + sqrt43, - 6 - sqrt43