(x-8)^2 + (x-1)^2 = x^2?

Question

Please help me solve this equation!!

Answer 1

Just expand the multiplications, collect terms, and solve like a normal quadratic equation.

x^2 - 16x + 64 + x^2 - 2x + 1 = x^2

x^2 - 18x + 65 = 0

(x - 5)(x - 13) = 0

x = 5 or 13

Answer 2

x ² - 16 x + 64 + x ² - 2 x + 1 = x ²

x ² - 18 x + 65 = 0

( x - 5 ) ( x - 13 ) = 0

x = 5 , x = 13

Answer 3

(x-8)^2+ (x-1)^2=x^2

x^2-16x+64+x^2-2x+1=x^2

2x^2-18x+65=x^2-x^2

x^2-18x+65=0

(x-5)(x-13)=0

x=5,13

Answer 4

(x-8)^2 + (x-1)^2 = x^2

x^2+64-16x+x^2+1-2x-x^2=0

x^2-18x+65=0

x=13

x=5

Answer 5

(x - 8)² + (x - 1)² = x²

(x² - 16x + 64) + (x² - 2x + 1) = x²

Combine like terms.

2x² - 18x + 65 = x²

x² - 18x + 65 = 0

(x - 5) (x - 13) = 0

x = 5, x = 13

Answer 6

(x-8)^2 + (x-1)^2 = x^2

x^2-16x+64+x^2-2x+1 = x^2

2(x^2) - 18x + 65 = x^2

x^2 - 18x + 65 = 0

Now use the quadratic equation.

(-b+/-(b^2-4ac)^(1/2))/2a  where a=1, b=(-18) and c=65.

so you should get 13 and 5 as answers.