What are the solutions to the equation x^2+(x+105)^2=195^2 ?

The solutions to the equation x^2+(x+105)^2=195^2 are x=75,x=-180

Find the zeros of x^2+(x+105)^2=195^2

The zeros of x^2+(x+105)^2=195^2 are x=75,x=-180

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x^{2} + (x + 105)^{2} = 19 5^{2}

x = 75, x = - 180

Solution steps

x^{2} + (x + 105)^{2} = 19 5^{2}

Expand

x^{2} + (x + 105)^{2} : 2 x^{2} + 210 x + 11025

Expand

19 5^{2} : 38025

2 x^{2} + 210 x + 11025 = 38025

Move

38025

to the left side

2 x^{2} + 210 x - 27000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 210 \pm 21 0 ^{2} - 4 \cdot 2 ( - 27000 )}{2 \cdot 2}

21 0^{2} - 4 \cdot 2 (- 27000) = 510

x_{1, 2} = \frac{- 210 \pm 510}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 210 + 510}{2 \cdot 2}, x_{2} = \frac{- 210 - 510}{2 \cdot 2}

x = \frac{- 210 + 510}{2 \cdot 2} : 75

x = \frac{- 210 - 510}{2 \cdot 2} : - 180

The solutions to the quadratic equation are:

x = 75, x = - 180

x + \frac{x}{3} = 4

- 5 (x - 10) = - 35

- 3 + 5 + 6 g = 11 - 3 g

2 x^{2} + 2 x - 12

3 x + 2 (4 x + 2) \geq 2 (6 x + 1)

What are the solutions to the equation x^2+(x+105)^2=195^2 ?
The solutions to the equation x^2+(x+105)^2=195^2 are x=75,x=-180
Find the zeros of x^2+(x+105)^2=195^2
The zeros of x^2+(x+105)^2=195^2 are x=75,x=-180