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

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

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

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

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

x = 13, x = 5

Solution steps

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

Expand

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

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

Switch sides

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^{2} + 7^{2} = n^{2}

2 x^{2} - 4 x + c^{2} - 2 c - 3 = 0

x^{2} + 6 x - 24 = 4 x - x^{2}

0 = x^{2} - 6 x + 12

x^{2} + 45 x + 600 = 0

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