What are the solutions to the equation (x-2)^2+(x-7)^2=x^2 ?

The solutions to the equation (x-2)^2+(x-7)^2=x^2 are x=9+2sqrt(7),x=9-2sqrt(7)

Find the zeros of (x-2)^2+(x-7)^2=x^2

The zeros of (x-2)^2+(x-7)^2=x^2 are x=9+2sqrt(7),x=9-2sqrt(7)

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(x - 2)^{2} + (x - 7)^{2} = x^{2}

x = 9 + 27, x = 9 - 27

Decimal Notation

x = 14.29150 \dots, x = 3.70849 \dots

Solution steps

(x - 2)^{2} + (x - 7)^{2} = x^{2}

Expand

(x - 2)^{2} + (x - 7)^{2} : 2 x^{2} - 18 x + 53

2 x^{2} - 18 x + 53 = x^{2}

Move

x^{2}

to the left side

x^{2} - 18 x + 53 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 1 \cdot 53}{2 \cdot 1}

(- 18)^{2} - 4 \cdot 1 \cdot 53 = 47

x_{1, 2} = \frac{- ( - 18 ) \pm 4 7}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 4 7}{2 \cdot 1}, x_{2} = \frac{- ( - 18 ) - 4 7}{2 \cdot 1}

x = \frac{- ( - 18 ) + 4 7}{2 \cdot 1} : 9 + 27

x = \frac{- ( - 18 ) - 4 7}{2 \cdot 1} : 9 - 27

The solutions to the quadratic equation are:

x = 9 + 27, x = 9 - 27

(x - 3)^{2} + (x + 7)^{2} = 49

\frac{x ^{2} + 6 x}{2} = 8

2 t^{2} - 7 t - 15 = 0

x^{2} + 15 x = - 54

3 x^{2} - 7 x - 9 = 0

What are the solutions to the equation (x-2)^2+(x-7)^2=x^2 ?
The solutions to the equation (x-2)^2+(x-7)^2=x^2 are x=9+2sqrt(7),x=9-2sqrt(7)
Find the zeros of (x-2)^2+(x-7)^2=x^2
The zeros of (x-2)^2+(x-7)^2=x^2 are x=9+2sqrt(7),x=9-2sqrt(7)