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

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

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

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

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(x - a)^{2} + x^{2} = 2 a^{2}

x = \frac{( 1 + 3 ) a}{2}, x = \frac{( 1 - 3 ) a}{2}

Solution steps

(x - a)^{2} + x^{2} = 2 a^{2}

Expand

(x - a)^{2} + x^{2} : 2 x^{2} - 2 a x + a^{2}

2 x^{2} - 2 a x + a^{2} = 2 a^{2}

Move

2 a^{2}

to the left side

2 x^{2} - 2 a x - a^{2} = 0

Solve with the quadratic formula

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

Simplify

(- 2 a)^{2} - 4 \cdot 2 (- a^{2}) : 23 a

x_{1, 2} = \frac{- ( - 2 a ) \pm 2 3 a}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 2 a ) + 2 3 a}{2 \cdot 2}, x_{2} = \frac{- ( - 2 a ) - 2 3 a}{2 \cdot 2}

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

x = \frac{- ( - 2 a ) - 2 3 a}{2 \cdot 2} : \frac{( 1 - 3 ) a}{2}

The solutions to the quadratic equation are:

x = \frac{( 1 + 3 ) a}{2}, x = \frac{( 1 - 3 ) a}{2}

4 x^{2} + x - 14 = 0

- 3 x^{2} + 9 x + 5

6 a^{2} + 2 a - 113 = - 9

x \frac{4 x - 3}{5} - \frac{2 x - 3}{2} = - 2

9 x (x + 1) 2 - 4 = 0

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