What are the solutions to the equation (x-2)^2+(x-9)^2=x^2 ?

The solutions to the equation (x-2)^2+(x-9)^2=x^2 are x=17,x=5

Find the zeros of (x-2)^2+(x-9)^2=x^2

The zeros of (x-2)^2+(x-9)^2=x^2 are x=17,x=5

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(x - 2)^{2} + (x - 9)^{2} = x^{2}

x = 17, x = 5

Solution steps

(x - 2)^{2} + (x - 9)^{2} = x^{2}

Expand

(x - 2)^{2} + (x - 9)^{2} : 2 x^{2} - 22 x + 85

2 x^{2} - 22 x + 85 = x^{2}

Move

x^{2}

to the left side

x^{2} - 22 x + 85 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 1 \cdot 85}{2 \cdot 1}

(- 22)^{2} - 4 \cdot 1 \cdot 85 = 12

x_{1, 2} = \frac{- ( - 22 ) \pm 12}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 22 ) + 12}{2 \cdot 1}, x_{2} = \frac{- ( - 22 ) - 12}{2 \cdot 1}

x = \frac{- ( - 22 ) + 12}{2 \cdot 1} : 17

x = \frac{- ( - 22 ) - 12}{2 \cdot 1} : 5

The solutions to the quadratic equation are:

x = 17, x = 5

3 (x - 5)^{2} - 81 = 0

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

x^{2} - 2 x = 0

x, x y^{4} + x^{2} y = x + 3 y

c, x^{2} - y^{2} = c^{2}

What are the solutions to the equation (x-2)^2+(x-9)^2=x^2 ?
The solutions to the equation (x-2)^2+(x-9)^2=x^2 are x=17,x=5
Find the zeros of (x-2)^2+(x-9)^2=x^2
The zeros of (x-2)^2+(x-9)^2=x^2 are x=17,x=5