What are the solutions to the equation 2-(x-5)^2=2x^2 ?

The solutions to the equation 2-(x-5)^2=2x^2 are x= 5/3-i(2sqrt(11))/3 ,x= 5/3+i(2sqrt(11))/3

Find the zeros of 2-(x-5)^2=2x^2

The zeros of 2-(x-5)^2=2x^2 are x= 5/3-i(2sqrt(11))/3 ,x= 5/3+i(2sqrt(11))/3

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2 - (x - 5)^{2} = 2 x^{2}

x = \frac{5}{3} - i \frac{2 11}{3}, x = \frac{5}{3} + i \frac{2 11}{3}

Solution steps

2 - (x - 5)^{2} = 2 x^{2}

Expand

2 - (x - 5)^{2} : - x^{2} + 10 x - 23

- x^{2} + 10 x - 23 = 2 x^{2}

Move

2 x^{2}

to the left side

- 3 x^{2} + 10 x - 23 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 ( - 3 ) ( - 23 )}{2 ( - 3 )}

Simplify

1 0^{2} - 4 (- 3) (- 23) : 411 i

x_{1, 2} = \frac{- 10 \pm 4 11 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 10 + 4 11 i}{2 ( - 3 )}, x_{2} = \frac{- 10 - 4 11 i}{2 ( - 3 )}

x = \frac{- 10 + 4 11 i}{2 ( - 3 )} : \frac{5}{3} - i \frac{2 11}{3}

x = \frac{- 10 - 4 11 i}{2 ( - 3 )} : \frac{5}{3} + i \frac{2 11}{3}

The solutions to the quadratic equation are:

x = \frac{5}{3} - i \frac{2 11}{3}, x = \frac{5}{3} + i \frac{2 11}{3}

z^{2} = \frac{1}{9}

2 x^{2} - 4 x - 1

2 x^{2} - 4 x + 4

(4 + 4) x^{2} - 3 \cdot 4 x + (4 - 1) = 0

5 x^{2} + 2 x - 8 = 16

What are the solutions to the equation 2-(x-5)^2=2x^2 ?
The solutions to the equation 2-(x-5)^2=2x^2 are x= 5/3-i(2sqrt(11))/3 ,x= 5/3+i(2sqrt(11))/3
Find the zeros of 2-(x-5)^2=2x^2
The zeros of 2-(x-5)^2=2x^2 are x= 5/3-i(2sqrt(11))/3 ,x= 5/3+i(2sqrt(11))/3