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

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

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

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

x = \frac{a ^{2} - 2 ab + b ^{2}}{2 ( a + b )}; a \neq = - b

Solution steps

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

Expand

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

Expand

2 a (a - b) : 2 a^{2} - 2 ab

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

Move

a^{2}

to the right side

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

Move

b^{2}

to the right side

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

Factor

2 a x + 2 b x : 2 x (a + b)

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

Divide both sides by

2 (a + b); a \neq = - b

x = \frac{a ^{2} - 2 ab + b ^{2}}{2 ( a + b )}; a \neq = - b

3 x - 15 = 17 - x

\frac{x}{5} + \frac{2 ( x - 4 )}{10} = 7

x, 3 x + 5 y = 3

x, 3 x + 5 y = 8

x, 5 x - y = 7

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