What are the solutions to the equation (x-8)^2+(x-1)^2=x^2 ?

The solutions to the equation (x-8)^2+(x-1)^2=x^2 are x=13,x=5

Find the zeros of (x-8)^2+(x-1)^2=x^2

The zeros of (x-8)^2+(x-1)^2=x^2 are x=13,x=5

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

x = 13, x = 5

Solution steps

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

Expand

(x - 8)^{2} + (x - 1)^{2} : 2 x^{2} - 18 x + 65

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

Move

x^{2}

to the left side

x^{2} - 18 x + 65 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 1 \cdot 65}{2 \cdot 1}

(- 18)^{2} - 4 \cdot 1 \cdot 65 = 8

x_{1, 2} = \frac{- ( - 18 ) \pm 8}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 8}{2 \cdot 1}, x_{2} = \frac{- ( - 18 ) - 8}{2 \cdot 1}

x = \frac{- ( - 18 ) + 8}{2 \cdot 1} : 13

x = \frac{- ( - 18 ) - 8}{2 \cdot 1} : 5

The solutions to the quadratic equation are:

x = 13, x = 5

4 x^{2} - 20 x + 21 = 0

x^{2} - 8 x + 17

d = \frac{1}{2} a t^{2}

- 4 x^{2} - 20 x - 25 = 0

3 x^{2} - 2 x - 2 = 4

What are the solutions to the equation (x-8)^2+(x-1)^2=x^2 ?
The solutions to the equation (x-8)^2+(x-1)^2=x^2 are x=13,x=5
Find the zeros of (x-8)^2+(x-1)^2=x^2
The zeros of (x-8)^2+(x-1)^2=x^2 are x=13,x=5