What is the answer to x^2+a^2=(a+x)^2-a(a-1) ?

The answer to x^2+a^2=(a+x)^2-a(a-1) is x=-(1-a)/2 ;\quad a\ne 0

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x^2+a^2=(a+x)^2-a(a-1)

x^{2} + a^{2} = (a + x)^{2} - a (a - 1)

x = - \frac{1 - a}{2}; a \neq = 0

Solution steps

x^{2} + a^{2} = (a + x)^{2} - a (a - 1)

Expand

(a + x)^{2} - a (a - 1) : x^{2} + 2 a x + a

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

Move

a^{2}

to the right side

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

Subtract

x^{2} + 2 a x

from both sides

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

Simplify

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

Divide both sides by

- 2 a; a \neq = 0

x = - \frac{1 - a}{2}; a \neq = 0

x - \frac{1}{3} = 2 x - \frac{7}{3}

x, 2 x y = 1

x, - 7 x + 5 y = 35

\frac{x}{2} = 10

x, 2 x + 3 y - 4 = 0

What is the answer to x^2+a^2=(a+x)^2-a(a-1) ?
The answer to x^2+a^2=(a+x)^2-a(a-1) is x=-(1-a)/2 ;\quad a\ne 0