What are the solutions to the equation (x-2)^2=-5x-8 ?

The solutions to the equation (x-2)^2=-5x-8 are x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2

Find the zeros of (x-2)^2=-5x-8

The zeros of (x-2)^2=-5x-8 are x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2

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(x - 2)^{2} = - 5 x - 8

x = - \frac{1}{2} + i \frac{47}{2}, x = - \frac{1}{2} - i \frac{47}{2}

Solution steps

(x - 2)^{2} = - 5 x - 8

Expand

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

x^{2} - 4 x + 4 = - 5 x - 8

Move

8

to the left side

x^{2} - 4 x + 12 = - 5 x

Move

5 x

to the left side

x^{2} + x + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 12}{2 \cdot 1}

Simplify

1^{2} - 4 \cdot 1 \cdot 12 : 47 i

x_{1, 2} = \frac{- 1 \pm 47 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 1 + 47 i}{2 \cdot 1}, x_{2} = \frac{- 1 - 47 i}{2 \cdot 1}

x = \frac{- 1 + 47 i}{2 \cdot 1} : - \frac{1}{2} + i \frac{47}{2}

x = \frac{- 1 - 47 i}{2 \cdot 1} : - \frac{1}{2} - i \frac{47}{2}

The solutions to the quadratic equation are:

x = - \frac{1}{2} + i \frac{47}{2}, x = - \frac{1}{2} - i \frac{47}{2}

\frac{1}{2} - \frac{3}{2}

36 - 8 x^{2} = 0

- 9 x + 5 < 17

12 x^{2} + 2 x - 4

\frac{4}{4 5}

What are the solutions to the equation (x-2)^2=-5x-8 ?
The solutions to the equation (x-2)^2=-5x-8 are x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2
Find the zeros of (x-2)^2=-5x-8
The zeros of (x-2)^2=-5x-8 are x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2