What are the solutions to the equation (x-1)^2+(x+4)^2=5 ?

The solutions to the equation (x-1)^2+(x+4)^2=5 are x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

Find the zeros of (x-1)^2+(x+4)^2=5

The zeros of (x-1)^2+(x+4)^2=5 are x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

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(x - 1)^{2} + (x + 4)^{2} = 5

x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Solution steps

(x - 1)^{2} + (x + 4)^{2} = 5

Expand

(x - 1)^{2} + (x + 4)^{2} : 2 x^{2} + 6 x + 17

2 x^{2} + 6 x + 17 = 5

Move

5

to the left side

2 x^{2} + 6 x + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 2 \cdot 12}{2 \cdot 2}

Simplify

6^{2} - 4 \cdot 2 \cdot 12 : 215 i

x_{1, 2} = \frac{- 6 \pm 2 15 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 6 + 2 15 i}{2 \cdot 2}, x_{2} = \frac{- 6 - 2 15 i}{2 \cdot 2}

x = \frac{- 6 + 2 15 i}{2 \cdot 2} : - \frac{3}{2} + i \frac{15}{2}

x = \frac{- 6 - 2 15 i}{2 \cdot 2} : - \frac{3}{2} - i \frac{15}{2}

The solutions to the quadratic equation are:

x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

x^{2} = 12 x - 36

1 6^{2} + 6 3^{2} = c^{2}

9 x^{2} + 18 x + 17 = 0

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

(x + 20) (x + 4) = 8 x - 1

What are the solutions to the equation (x-1)^2+(x+4)^2=5 ?
The solutions to the equation (x-1)^2+(x+4)^2=5 are x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2
Find the zeros of (x-1)^2+(x+4)^2=5
The zeros of (x-1)^2+(x+4)^2=5 are x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2