Factoring x squared - 64 = 0

For this explanation, I'm going to write x squared as x^2.

This is whats called a "difference of squares" question. They appear whenever you have a squared x term (x^2), followed by a subtraction sign and a "perfect square" such as 4, 9, 25, 81, etc. It's actually very easy to factor! Determine the square root of the real number (in this case 64, whose square root is 8), then write two terms containing that number and a non-squared x. In one term separate them with a +, and the other with a -.

x^2 - 64 = 0

becomes

(x-8) (x+8) = 0

If you can remember your perfect squares, and can identify a question as a "difference of squares" question, they are really easy!

Since - 64 - 64 does not contain the variable to solve for, move it to the right side of the equation by adding 6464 to both sides. x2 = 64 x2 = 64 Take the square root of both sides of the equation to eliminate the exponent on the left side. x = ± √64 x = ±64 The complete solution is the result of both the positive and negative portions of the solution.

x=8, - 8