What are the solutions to the equation (x+5)^2+(x-8)^2=25 ?

The solutions to the equation (x+5)^2+(x-8)^2=25 are x= 3/2+i(sqrt(119))/2 ,x= 3/2-i(sqrt(119))/2

Find the zeros of (x+5)^2+(x-8)^2=25

The zeros of (x+5)^2+(x-8)^2=25 are x= 3/2+i(sqrt(119))/2 ,x= 3/2-i(sqrt(119))/2

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(x + 5)^{2} + (x - 8)^{2} = 25

x = \frac{3}{2} + i \frac{119}{2}, x = \frac{3}{2} - i \frac{119}{2}

Solution steps

(x + 5)^{2} + (x - 8)^{2} = 25

Expand

(x + 5)^{2} + (x - 8)^{2} : 2 x^{2} - 6 x + 89

2 x^{2} - 6 x + 89 = 25

Move

25

to the left side

2 x^{2} - 6 x + 64 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 \cdot 64}{2 \cdot 2}

Simplify

(- 6)^{2} - 4 \cdot 2 \cdot 64 : 2119 i

x_{1, 2} = \frac{- ( - 6 ) \pm 2 119 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 119 i}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 119 i}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 119 i}{2 \cdot 2} : \frac{3}{2} + i \frac{119}{2}

x = \frac{- ( - 6 ) - 2 119 i}{2 \cdot 2} : \frac{3}{2} - i \frac{119}{2}

The solutions to the quadratic equation are:

x = \frac{3}{2} + i \frac{119}{2}, x = \frac{3}{2} - i \frac{119}{2}

(x - 3)^{2} - (2 x + 5)^{2} = - 26 x - 28

c^{2} - 9 c + 11 = 0

3 x^{2} - 6 = (x + 2) (x - 3)

8 f^{2} + 11 f = 2 f^{2} + 3 (2 f - 5) + 21

y, 3 y - 2 x y - 3 y^{2} = 0

What are the solutions to the equation (x+5)^2+(x-8)^2=25 ?
The solutions to the equation (x+5)^2+(x-8)^2=25 are x= 3/2+i(sqrt(119))/2 ,x= 3/2-i(sqrt(119))/2
Find the zeros of (x+5)^2+(x-8)^2=25
The zeros of (x+5)^2+(x-8)^2=25 are x= 3/2+i(sqrt(119))/2 ,x= 3/2-i(sqrt(119))/2