What are the solutions to the equation (2-x)^2-(2x-3)^2=50 ?

The solutions to the equation (2-x)^2-(2x-3)^2=50 are x= 4/3-i(sqrt(149))/3 ,x= 4/3+i(sqrt(149))/3

Find the zeros of (2-x)^2-(2x-3)^2=50

The zeros of (2-x)^2-(2x-3)^2=50 are x= 4/3-i(sqrt(149))/3 ,x= 4/3+i(sqrt(149))/3

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(2 - x)^{2} - (2 x - 3)^{2} = 50

x = \frac{4}{3} - i \frac{149}{3}, x = \frac{4}{3} + i \frac{149}{3}

Solution steps

(2 - x)^{2} - (2 x - 3)^{2} = 50

Expand

(2 - x)^{2} - (2 x - 3)^{2} : - 3 x^{2} + 8 x - 5

- 3 x^{2} + 8 x - 5 = 50

Move

50

to the left side

- 3 x^{2} + 8 x - 55 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 ( - 3 ) ( - 55 )}{2 ( - 3 )}

Simplify

8^{2} - 4 (- 3) (- 55) : 2149 i

x_{1, 2} = \frac{- 8 \pm 2 149 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 8 + 2 149 i}{2 ( - 3 )}, x_{2} = \frac{- 8 - 2 149 i}{2 ( - 3 )}

x = \frac{- 8 + 2 149 i}{2 ( - 3 )} : \frac{4}{3} - i \frac{149}{3}

x = \frac{- 8 - 2 149 i}{2 ( - 3 )} : \frac{4}{3} + i \frac{149}{3}

The solutions to the quadratic equation are:

x = \frac{4}{3} - i \frac{149}{3}, x = \frac{4}{3} + i \frac{149}{3}

(5 - x)^{2} - (3 x - 1)^{2} = 0

(y + 2)^{2} = - 9

(x + 2) (2 x - 3) = 3 x - 7

3 x - (2 - x) - 2 = (x + 1) (2 - 3 x)

x^{2} - 7 x - 10 = - 2 x - 4

What are the solutions to the equation (2-x)^2-(2x-3)^2=50 ?
The solutions to the equation (2-x)^2-(2x-3)^2=50 are x= 4/3-i(sqrt(149))/3 ,x= 4/3+i(sqrt(149))/3
Find the zeros of (2-x)^2-(2x-3)^2=50
The zeros of (2-x)^2-(2x-3)^2=50 are x= 4/3-i(sqrt(149))/3 ,x= 4/3+i(sqrt(149))/3