The Square Root Property and Completing the Square Chapter 8 Section 1 The Square Root Property and Completing the Square

Question If x2 = 25, what is the x value? How many solutions?

Solve the equation

Solve (x – 1)2 = 5 Note: If one can get the term squared, then taking the square root of both sides will . . .

Completing the Square Completing the square will allow one to write a binomial squared, then the solution will come. To complete the square, observe x2 + 6x + 9 (x)2 (3)2 2(x)(3)

Observe Complete the square: half 10 and square x2 – 10x Half 10 is 5 and square is 25 Thus, x2 – 10x + 25 Factor: (x – 5)2

Determine the constant that should be added so that the binomial becomes a perfect square trinomial 4) 5) 6)

Next Once one complete the square, one can now solve the equation: x2 – 10x = 0 x2 – 10x + 25 = 25 (x – 5)2 = 25 x - 5 = x =10 or 0

Solve the equation

Summary Use square root property to solve equations Complete the square Complete the square to solve equations.