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

The solutions to the equation (x-2)^2+(x+4)^2=1 are x=-1+isqrt(17/2),x=-1-isqrt(17/2)

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

The zeros of (x-2)^2+(x+4)^2=1 are x=-1+isqrt(17/2),x=-1-isqrt(17/2)

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

x = - 1 + i \frac{17}{2}, x = - 1 - i \frac{17}{2}

Solution steps

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

Expand

(x - 2)^{2} + (x + 4)^{2} : 2 x^{2} + 4 x + 20

2 x^{2} + 4 x + 20 = 1

Move

1

to the left side

2 x^{2} + 4 x + 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 2 \cdot 19}{2 \cdot 2}

Simplify

4^{2} - 4 \cdot 2 \cdot 19 : 234 i

x_{1, 2} = \frac{- 4 \pm 2 34 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 4 + 2 34 i}{2 \cdot 2}, x_{2} = \frac{- 4 - 2 34 i}{2 \cdot 2}

x = \frac{- 4 + 2 34 i}{2 \cdot 2} : - 1 + i \frac{17}{2}

x = \frac{- 4 - 2 34 i}{2 \cdot 2} : - 1 - i \frac{17}{2}

The solutions to the quadratic equation are:

x = - 1 + i \frac{17}{2}, x = - 1 - i \frac{17}{2}

2 x^{2} + 8 x = 10

3 x^{2} - 15 = - 378

t^{2} + 4 t + 3 = 0

5 x^{2} - 85 = 40

x, x^{2} y - x^{2} + 4 y = 0

What are the solutions to the equation (x-2)^2+(x+4)^2=1 ?
The solutions to the equation (x-2)^2+(x+4)^2=1 are x=-1+isqrt(17/2),x=-1-isqrt(17/2)
Find the zeros of (x-2)^2+(x+4)^2=1
The zeros of (x-2)^2+(x+4)^2=1 are x=-1+isqrt(17/2),x=-1-isqrt(17/2)