What are the solutions to the equation (x-3)^2+(-x+7)^2=16 ?

The solutions to the equation (x-3)^2+(-x+7)^2=16 are x=7,x=3

Find the zeros of (x-3)^2+(-x+7)^2=16

The zeros of (x-3)^2+(-x+7)^2=16 are x=7,x=3

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(x - 3)^{2} + (- x + 7)^{2} = 16

x = 7, x = 3

Solution steps

(x - 3)^{2} + (- x + 7)^{2} = 16

Expand

(x - 3)^{2} + (- x + 7)^{2} : 2 x^{2} - 20 x + 58

2 x^{2} - 20 x + 58 = 16

Move

16

to the left side

2 x^{2} - 20 x + 42 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 2 \cdot 42}{2 \cdot 2}

(- 20)^{2} - 4 \cdot 2 \cdot 42 = 8

x_{1, 2} = \frac{- ( - 20 ) \pm 8}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 8}{2 \cdot 2}, x_{2} = \frac{- ( - 20 ) - 8}{2 \cdot 2}

x = \frac{- ( - 20 ) + 8}{2 \cdot 2} : 7

x = \frac{- ( - 20 ) - 8}{2 \cdot 2} : 3

The solutions to the quadratic equation are:

x = 7, x = 3

x^{2} + 2 x - \frac{5}{4} = 0

5^{2} + x^{2} = 9^{2}

x, 3 x^{2} + 4 x y + 6 y^{2} = 140

x^{2} - 21 = - 38

64 s^{2} + 8 s + 25 = 0

What are the solutions to the equation (x-3)^2+(-x+7)^2=16 ?
The solutions to the equation (x-3)^2+(-x+7)^2=16 are x=7,x=3
Find the zeros of (x-3)^2+(-x+7)^2=16
The zeros of (x-3)^2+(-x+7)^2=16 are x=7,x=3