What are the solutions to the equation (x-2)^2-(2x+3)^2=80 ?

The solutions to the equation (x-2)^2-(2x+3)^2=80 are x=-8/3-i(sqrt(191))/3 ,x=-8/3+i(sqrt(191))/3

Find the zeros of (x-2)^2-(2x+3)^2=80

The zeros of (x-2)^2-(2x+3)^2=80 are x=-8/3-i(sqrt(191))/3 ,x=-8/3+i(sqrt(191))/3

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(x - 2)^{2} - (2 x + 3)^{2} = 80

x = - \frac{8}{3} - i \frac{191}{3}, x = - \frac{8}{3} + i \frac{191}{3}

Solution steps

(x - 2)^{2} - (2 x + 3)^{2} = 80

Expand

(x - 2)^{2} - (2 x + 3)^{2} : - 3 x^{2} - 16 x - 5

- 3 x^{2} - 16 x - 5 = 80

Move

80

to the left side

- 3 x^{2} - 16 x - 85 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 ( - 3 ) ( - 85 )}{2 ( - 3 )}

Simplify

(- 16)^{2} - 4 (- 3) (- 85) : 2191 i

x_{1, 2} = \frac{- ( - 16 ) \pm 2 191 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 16 ) + 2 191 i}{2 ( - 3 )}, x_{2} = \frac{- ( - 16 ) - 2 191 i}{2 ( - 3 )}

x = \frac{- ( - 16 ) + 2 191 i}{2 ( - 3 )} : - \frac{8}{3} - i \frac{191}{3}

x = \frac{- ( - 16 ) - 2 191 i}{2 ( - 3 )} : - \frac{8}{3} + i \frac{191}{3}

The solutions to the quadratic equation are:

x = - \frac{8}{3} - i \frac{191}{3}, x = - \frac{8}{3} + i \frac{191}{3}

x, 5 x^{2} + 2 x y - 2 y^{2} - x + 3 y + 6 = 0

- 6 p - 27 = - p^{2}

x^{2} - (a + d) x + (a d - b c) = 0

9 x^{2} - 5 x = 0

25 + 8 x - x^{2} = 0

What are the solutions to the equation (x-2)^2-(2x+3)^2=80 ?
The solutions to the equation (x-2)^2-(2x+3)^2=80 are x=-8/3-i(sqrt(191))/3 ,x=-8/3+i(sqrt(191))/3
Find the zeros of (x-2)^2-(2x+3)^2=80
The zeros of (x-2)^2-(2x+3)^2=80 are x=-8/3-i(sqrt(191))/3 ,x=-8/3+i(sqrt(191))/3