What are the solutions to the equation x^2+(x+140)^2=340^2 ?

The solutions to the equation x^2+(x+140)^2=340^2 are x=160,x=-300

Find the zeros of x^2+(x+140)^2=340^2

The zeros of x^2+(x+140)^2=340^2 are x=160,x=-300

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x^{2} + (x + 140)^{2} = 34 0^{2}

x = 160, x = - 300

Solution steps

x^{2} + (x + 140)^{2} = 34 0^{2}

Expand

x^{2} + (x + 140)^{2} : 2 x^{2} + 280 x + 19600

Expand

34 0^{2} : 115600

2 x^{2} + 280 x + 19600 = 115600

Move

115600

to the left side

2 x^{2} + 280 x - 96000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 280 \pm 28 0 ^{2} - 4 \cdot 2 ( - 96000 )}{2 \cdot 2}

28 0^{2} - 4 \cdot 2 (- 96000) = 920

x_{1, 2} = \frac{- 280 \pm 920}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 280 + 920}{2 \cdot 2}, x_{2} = \frac{- 280 - 920}{2 \cdot 2}

x = \frac{- 280 + 920}{2 \cdot 2} : 160

x = \frac{- 280 - 920}{2 \cdot 2} : - 300

The solutions to the quadratic equation are:

x = 160, x = - 300

n^{2} + 4 n - 572 = 0

x, x^{2} + y^{2} - 8 x - 6 y + 28 = 0

2 x^{2} - 4 x = 2

(2 x - 3) (2 x + 6) = 0

8 x^{2} + 9 x - 3 = 0

What are the solutions to the equation x^2+(x+140)^2=340^2 ?
The solutions to the equation x^2+(x+140)^2=340^2 are x=160,x=-300
Find the zeros of x^2+(x+140)^2=340^2
The zeros of x^2+(x+140)^2=340^2 are x=160,x=-300