What are the solutions to the equation x^2-(x-2)^2-(x-4)^2=7 ?

The solutions to the equation x^2-(x-2)^2-(x-4)^2=7 are x=3,x=9

Find the zeros of x^2-(x-2)^2-(x-4)^2=7

The zeros of x^2-(x-2)^2-(x-4)^2=7 are x=3,x=9

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x^{2} - (x - 2)^{2} - (x - 4)^{2} = 7

x = 3, x = 9

Solution steps

x^{2} - (x - 2)^{2} - (x - 4)^{2} = 7

Expand

x^{2} - (x - 2)^{2} - (x - 4)^{2} : - x^{2} + 12 x - 20

- x^{2} + 12 x - 20 = 7

Move

7

to the left side

- x^{2} + 12 x - 27 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 ( - 1 ) ( - 27 )}{2 ( - 1 )}

1 2^{2} - 4 (- 1) (- 27) = 6

x_{1, 2} = \frac{- 12 \pm 6}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 12 + 6}{2 ( - 1 )}, x_{2} = \frac{- 12 - 6}{2 ( - 1 )}

x = \frac{- 12 + 6}{2 ( - 1 )} : 3

x = \frac{- 12 - 6}{2 ( - 1 )} : 9

The solutions to the quadratic equation are:

x = 3, x = 9

(\frac{4}{49})^{\frac{3}{2}}

t (44 - 0.8 t) = 0

- 4 y = 2 y^{2} - 6

\frac{( 8 c + 44 )}{( c + 6 )}

(- 1)^{- 5}

What are the solutions to the equation x^2-(x-2)^2-(x-4)^2=7 ?
The solutions to the equation x^2-(x-2)^2-(x-4)^2=7 are x=3,x=9
Find the zeros of x^2-(x-2)^2-(x-4)^2=7
The zeros of x^2-(x-2)^2-(x-4)^2=7 are x=3,x=9