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

The answer to (x+a)^2=(x-a)^2+(a+b)^2 is x=(a^2+b^2+2ab)/(4a);\quad a\ne 0

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

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

x = \frac{a ^{2} + b ^{2} + 2 ab}{4 a}; a \neq = 0

Solution steps

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

Expand

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

Expand

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

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

Move

a^{2}

to the right side

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

Subtract

x^{2} - 2 a x

from both sides

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

Simplify

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

Divide both sides by

4 a; a \neq = 0

x = \frac{a ^{2} + b ^{2} + 2 ab}{4 a}; a \neq = 0

m, f = x^{3} + m x^{2} - 9 x + 1

\frac{3 x}{2} + 6 = 0

M = 2 0^{\circ} - 2 0^{\circ} + \frac{3}{8} π

D, N (D) = 4 (D - 28) + 14

\frac{2 ( 5 x + 2 )}{9} - \frac{4 x - 1}{2} = \frac{x}{1}

What is the answer to (x+a)^2=(x-a)^2+(a+b)^2 ?
The answer to (x+a)^2=(x-a)^2+(a+b)^2 is x=(a^2+b^2+2ab)/(4a);\quad a\ne 0