PreCalculus Notes: Completing the Square CS-1
Perfect Square Trinomials
Factor
x + 2x +1 =
Completing the square
x + 2x =
x2 + 6 x + 9 =
x2 + 6x =
2
2
x 2 − 16 x + 64 =
x 2 − 16 x =
We want to know how to make the binomial x 2 + bx into a perfect square trinomial. In other words, if we know
b, find c and k so that
x 2 + bx + c = ( x + k )
x 2 + bx
2
= (x + k) −c
2
Ex: Complete the square: x 2 + 12 x
Ex: Complete the square: x 2 − 10 x
Ex: Complete the square: x 2 − 5 x
Ex: Rewrite using a perfect square trinomial: y =
1
x − 8x + 7
2
Ex: Rewrite using a perfect square: y = 2 x 2 − 24 x − 5
Ex: Rewrite using a perfect square: y = −2 x 2 + 20 x − 35
Ex: Rewrite using two perfect squares: 4 x 2 − y 2 + 24 x + 14 y − 29 = 0
Ex: Solve for y: 3 x = y 2 − 4 y + 5