What are the solutions to the equation (x-3)^2+(x+7)^2=49 ?

The solutions to the equation (x-3)^2+(x+7)^2=49 are x=-2+i(sqrt(2))/2 ,x=-2-i(sqrt(2))/2

Find the zeros of (x-3)^2+(x+7)^2=49

The zeros of (x-3)^2+(x+7)^2=49 are x=-2+i(sqrt(2))/2 ,x=-2-i(sqrt(2))/2

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(x - 3)^{2} + (x + 7)^{2} = 49

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

Solution steps

(x - 3)^{2} + (x + 7)^{2} = 49

Expand

(x - 3)^{2} + (x + 7)^{2} : 2 x^{2} + 8 x + 58

2 x^{2} + 8 x + 58 = 49

Move

49

to the left side

2 x^{2} + 8 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 2 \cdot 9}{2 \cdot 2}

Simplify

8^{2} - 4 \cdot 2 \cdot 9 : 22 i

x_{1, 2} = \frac{- 8 \pm 2 2 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 8 + 2 2 i}{2 \cdot 2}, x_{2} = \frac{- 8 - 2 2 i}{2 \cdot 2}

x = \frac{- 8 + 2 2 i}{2 \cdot 2} : - 2 + i \frac{2}{2}

x = \frac{- 8 - 2 2 i}{2 \cdot 2} : - 2 - i \frac{2}{2}

The solutions to the quadratic equation are:

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

\frac{x ^{2} + 6 x}{2} = 8

2 t^{2} - 7 t - 15 = 0

x^{2} + 15 x = - 54

3 x^{2} - 7 x - 9 = 0

(m^{2} - 1) x^{2} + 9 = 2 (3 m + 1) x

What are the solutions to the equation (x-3)^2+(x+7)^2=49 ?
The solutions to the equation (x-3)^2+(x+7)^2=49 are x=-2+i(sqrt(2))/2 ,x=-2-i(sqrt(2))/2
Find the zeros of (x-3)^2+(x+7)^2=49
The zeros of (x-3)^2+(x+7)^2=49 are x=-2+i(sqrt(2))/2 ,x=-2-i(sqrt(2))/2