What are the solutions to the equation (26-x)^2+(13-x)^2=x^2 ?

The solutions to the equation (26-x)^2+(13-x)^2=x^2 are x=65,x=13

Find the zeros of (26-x)^2+(13-x)^2=x^2

The zeros of (26-x)^2+(13-x)^2=x^2 are x=65,x=13

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(26 - x)^{2} + (13 - x)^{2} = x^{2}

x = 65, x = 13

Solution steps

(26 - x)^{2} + (13 - x)^{2} = x^{2}

Expand

(26 - x)^{2} + (13 - x)^{2} : 2 x^{2} - 78 x + 845

2 x^{2} - 78 x + 845 = x^{2}

Move

x^{2}

to the left side

x^{2} - 78 x + 845 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 78 ) \pm ( - 78 ) ^{2} - 4 \cdot 1 \cdot 845}{2 \cdot 1}

(- 78)^{2} - 4 \cdot 1 \cdot 845 = 52

x_{1, 2} = \frac{- ( - 78 ) \pm 52}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 78 ) + 52}{2 \cdot 1}, x_{2} = \frac{- ( - 78 ) - 52}{2 \cdot 1}

x = \frac{- ( - 78 ) + 52}{2 \cdot 1} : 65

x = \frac{- ( - 78 ) - 52}{2 \cdot 1} : 13

The solutions to the quadratic equation are:

x = 65, x = 13

2 (x + 3)^{2} = 0

(x + 2) (3 x - 1) = (x - 5)^{2}

(4 + 3 x)^{2} + x^{2} = 146

7 x^{2} + 8 x - 9 = 10

- 5 x^{2} + 11 x + 36 = 0

What are the solutions to the equation (26-x)^2+(13-x)^2=x^2 ?
The solutions to the equation (26-x)^2+(13-x)^2=x^2 are x=65,x=13
Find the zeros of (26-x)^2+(13-x)^2=x^2
The zeros of (26-x)^2+(13-x)^2=x^2 are x=65,x=13