What are the solutions to the equation (x+5)^2+(x-2)^2=37 ?

The solutions to the equation (x+5)^2+(x-2)^2=37 are x=1,x=-4

Find the zeros of (x+5)^2+(x-2)^2=37

The zeros of (x+5)^2+(x-2)^2=37 are x=1,x=-4

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(x + 5)^{2} + (x - 2)^{2} = 37

x = 1, x = - 4

Solution steps

(x + 5)^{2} + (x - 2)^{2} = 37

Expand

(x + 5)^{2} + (x - 2)^{2} : 2 x^{2} + 6 x + 29

2 x^{2} + 6 x + 29 = 37

Move

37

to the left side

2 x^{2} + 6 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 2 ( - 8 )}{2 \cdot 2}

6^{2} - 4 \cdot 2 (- 8) = 10

x_{1, 2} = \frac{- 6 \pm 10}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 6 + 10}{2 \cdot 2}, x_{2} = \frac{- 6 - 10}{2 \cdot 2}

x = \frac{- 6 + 10}{2 \cdot 2} : 1

x = \frac{- 6 - 10}{2 \cdot 2} : - 4

The solutions to the quadratic equation are:

x = 1, x = - 4

a x^{2} + c = 0

4 x^{2} - 4 x + 3

2 x^{2} - 12 x + 16 = 0

x^{2} - 5 x + 6 = 0

5 x^{2} - 500 = 0

What are the solutions to the equation (x+5)^2+(x-2)^2=37 ?
The solutions to the equation (x+5)^2+(x-2)^2=37 are x=1,x=-4
Find the zeros of (x+5)^2+(x-2)^2=37
The zeros of (x+5)^2+(x-2)^2=37 are x=1,x=-4