Transposition of formulae

Question

Transposition of formulae

Solve the equation f(x) = 0 for each of the following quadratic functions:

1.  f(x)=−x2 +22x−85
2.  f(x)=x2 −18x+81

Please helpppp?

Answer 1

1. x^2 + 22x + 121 - 85 = (x-11)^2 = 36, x=11+ or - 6, x=17 or 5
2. x^2 - 18x + 81, (x-9)^2 = 0 x = 9

It's called "completing the square" method. You take half the coefficient of the x term. --22/2 = 11. Then square it to get (-11)^2 = 121. add 121 to both sides

1. f(x) = -x^2 + 22x - 85 = 0. multiply by negative one to make the x^2 term positive

x^2 - 22x + 85=0

x^2 - 22x + 121 = -85 + 121, = 36 = 6^2

now put the left side in squared form

(x-11)^2 = 6^2 or (-6)^2

take the square roots of both sides

x-11 = 6 or -6

add 11 to both sides

x= 17 or 5

2 x^2 -18x +81. take half of -18 and square it, (-9)^2 to get 81. It's already in squared form

(x-9)^2 = 0 take the square root of both sides

x-9 =0

add 9 to both sides

x=9