What are the solutions to the equation 2x^2+(x+5)^2=10^2 ?

The solutions to the equation 2x^2+(x+5)^2=10^2 are x=(5(sqrt(10)-1))/3 ,x=-(5(1+sqrt(10)))/3

Find the zeros of 2x^2+(x+5)^2=10^2

The zeros of 2x^2+(x+5)^2=10^2 are x=(5(sqrt(10)-1))/3 ,x=-(5(1+sqrt(10)))/3

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2 x^{2} + (x + 5)^{2} = 1 0^{2}

x = \frac{5 ( 10 - 1 )}{3}, x = - \frac{5 ( 1 + 10 )}{3}

Decimal Notation

x = 3.60379 \dots, x = - 6.93712 \dots

Solution steps

2 x^{2} + (x + 5)^{2} = 1 0^{2}

Expand

2 x^{2} + (x + 5)^{2} : 3 x^{2} + 10 x + 25

Expand

1 0^{2} : 100

3 x^{2} + 10 x + 25 = 100

Move

100

to the left side

3 x^{2} + 10 x - 75 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 \cdot 3 ( - 75 )}{2 \cdot 3}

1 0^{2} - 4 \cdot 3 (- 75) = 1010

x_{1, 2} = \frac{- 10 \pm 10 10}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 10 + 10 10}{2 \cdot 3}, x_{2} = \frac{- 10 - 10 10}{2 \cdot 3}

x = \frac{- 10 + 10 10}{2 \cdot 3} : \frac{5 ( 10 - 1 )}{3}

x = \frac{- 10 - 10 10}{2 \cdot 3} : - \frac{5 ( 1 + 10 )}{3}

The solutions to the quadratic equation are:

x = \frac{5 ( 10 - 1 )}{3}, x = - \frac{5 ( 1 + 10 )}{3}

\frac{5 x + 1}{6} + \frac{2 x + 1}{3} = 2

3 x^{2} - x - 6 = 0

\frac{5}{4} - \frac{1}{2}

2 x - 11 \geq 5

(\frac{n - 1}{n})^{2}

What are the solutions to the equation 2x^2+(x+5)^2=10^2 ?
The solutions to the equation 2x^2+(x+5)^2=10^2 are x=(5(sqrt(10)-1))/3 ,x=-(5(1+sqrt(10)))/3
Find the zeros of 2x^2+(x+5)^2=10^2
The zeros of 2x^2+(x+5)^2=10^2 are x=(5(sqrt(10)-1))/3 ,x=-(5(1+sqrt(10)))/3