Square Root & Complete the Square

The square root of a number 'x' is a value 'y' such that y² = x. It can be positive or negative.

To solve an equation by taking the square root, isolate the squared term on one side of the equation and then take the square root of both sides.

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form (a + b)² = a² + 2ab + b².

To create a perfect square trinomial from x² + bx, take half of 'b', square it, and add it to the expression.

If x² = k, then x = ±√k.

To solve x² = 121, take the square root of both sides to get x = ±11.

The ± symbol indicates that there are two possible solutions: one positive and one negative.

First, isolate m² by adding 100 to both sides, then divide by 4, and finally take the square root to find m = ±5.

Completing the square involves rewriting a quadratic equation in the form (x + p)² = q, making it easier to solve.

Take the square root of both sides to get x + 6 = ±7, then solve for x to find x = 1 and x = -13.