3 8-1 Completing the Square Square Root Property:If c > 0, the equation x2 = c has TWO solutions:x = or x = –(Use when there is an x2 term and another number)Move constant over to other sideFind the square root of both sidesUse the square root property to find the answersExample 3a: Solve: x2 – 12 = 0
6 8-1 Completing the Square Example 7: Add a number to make each binomial a perfect square:x2 + 10xx2 – 6xStepsFind ½ of the coefficient of the x termSquare itAdd it the equation
7 8-1 Completing the Square When the coefficient of x is 1:If necessary, move the number to other side of the equation to put it on the right side of the equal sign.Complete the square:Find ½ of the coefficient of the x term and square it.Add the square to both sides of the equation.Factor the trinomial square on the left.Solve the resulting equation using the square root property.
8 8-1 Completing the Square Example 8a:Use completing the square to solve:x2 + 8x + 7 = 0
9 8-1 Completing the Square Example 8b:Use completing the square to solve:a2 + 5a + 4 = 0