What are the solutions to the equation (18-x)^2+(9-x)^2=x^2 ?

The solutions to the equation (18-x)^2+(9-x)^2=x^2 are x=45,x=9

Find the zeros of (18-x)^2+(9-x)^2=x^2

The zeros of (18-x)^2+(9-x)^2=x^2 are x=45,x=9

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

x = 45, x = 9

Solution steps

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

Expand

(18 - x)^{2} + (9 - x)^{2} : 2 x^{2} - 54 x + 405

2 x^{2} - 54 x + 405 = x^{2}

Move

x^{2}

to the left side

x^{2} - 54 x + 405 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 54 ) \pm ( - 54 ) ^{2} - 4 \cdot 1 \cdot 405}{2 \cdot 1}

(- 54)^{2} - 4 \cdot 1 \cdot 405 = 36

x_{1, 2} = \frac{- ( - 54 ) \pm 36}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 54 ) + 36}{2 \cdot 1}, x_{2} = \frac{- ( - 54 ) - 36}{2 \cdot 1}

x = \frac{- ( - 54 ) + 36}{2 \cdot 1} : 45

x = \frac{- ( - 54 ) - 36}{2 \cdot 1} : 9

The solutions to the quadratic equation are:

x = 45, x = 9

3 x^{2} + 2 x = x^{2} + 3 x + 6

x^{2} + \frac{5}{2} x - 9 = 0

x^{2} - 5 x = 2 x^{2} + x

\frac{x ^{2}}{3} - 8 x - 18 = 0

2 c^{2} + 4 c - 6 = - 3 c

What are the solutions to the equation (18-x)^2+(9-x)^2=x^2 ?
The solutions to the equation (18-x)^2+(9-x)^2=x^2 are x=45,x=9
Find the zeros of (18-x)^2+(9-x)^2=x^2
The zeros of (18-x)^2+(9-x)^2=x^2 are x=45,x=9