(x-4)^2 = 9x?

Hi,

(x - 4)² = 9x
x² - 8x + 16 = 9x
x² - 17x = -16
Multiply ½ x -17 = -17/2
Square -17/2 and add 289/4 to both sides.

x² - 17x + 289/4 = -16 + 289/4

Factor the left and combine like terms on the right.

(x - 17/2)² = 225/4
Take the square root on both sides, putting ± in front of the radical on the right.
..________.........____
√(x - 17/2)² = ± √225/4

x - 17/2 = ± 15/2
x = 17/2 ± 15/2
x = 17/2 + 15/2 = 16 <== ANSWER
x = 17/2 - 15/2 = 1 <== ANSWER

16 and 1 are the answers.

I hope that helps!! :-)

(x - 4)(x - 4) - 9x = 0
x² - 8x + 16 - 9x = 0
x² - 17x + 16 = 0
(x - 1)(x - 16) = 0
x = 1 , x = 16

(x-4)^2=9x
x^2-8x-9x+16=9x-9x
x^2-17x+16=0
(x-16)(x-1)=0
x-16=0
x=16

x-1=0
x=1

(x-4)^2 = 9x
x^2+(4)^2-(2*4*x) = 9x
x^2+16-8x = 9x
x^2+16-8x-9x=0
x^2-17x+16=0
x^2-16x-x+16=0
x(x-16)-1(x-16)=0
(x-16)(x-1)=0

(x - 4)^2 = 9x
(x - 4)(x - 4) = 9x
x^2 - 4x - 4x + 16 = 9x
x^2 + 16 = 9x + 8x
x^2 + 16 = 17x
x^2 - 17x + 16 = 0
(x - 1)(x - 16) = 0

x - 1 = 0
x = 1

x - 16 = 0
x = 16

∴ x = 1 or 16

(x - 4)^2 = 9x
x^2 - 8x + 16 - 9x = 0
x^2 -17x + 16 = 0
x^2 - 17x +(-17/2)^2 - (-17/2)^2 + 16 = 0
(x - 17/2)^2 -(289/4) + 16 = 0
(x - 17/2)^2 = 225/4
(x - 17/2) = 15/2 @ -15/2
x=17/2+15/2 @ 17/2 -15/2
x = 16 @ 1

(x - 4)^2 = 9x

(x - 4)^2 - 9x = 0

x^2 - 8x + 16 - 9x = 0
x^2 - 17x + 16 = 0

It would be much faster to solve it by the factoring method, but whatever.

x^2 - 17x + (17^2)/4 + 16 - (17^2)/4 = 0
[x - (17/2)]^2 + 48/4 - (17^2)/4 = 0
[x - (17/2)]^2 = (17^2)/4 - 48/4

And you can take it from here.