What is the answer to (x+b)^2-(x-a)^2-(a+b)^2=0 ?

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

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(x+b)^2-(x-a)^2-(a+b)^2=0

(x + b)^{2} - (x - a)^{2} - (a + b)^{2} = 0

x = a; b \neq = - a

Solution steps

(x + b)^{2} - (x - a)^{2} - (a + b)^{2} = 0

Move

(a + b)^{2}

to the right side

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

Expand

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

Expand

(b + a)^{2} : b^{2} + 2 ba + a^{2}

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

Move

b^{2}

to the right side

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

Move

a^{2}

to the right side

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

Factor

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

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

Divide both sides by

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

x = a; b \neq = - a

- 4 (- 3 p + 6) - 5 p = 10 p

x, 3 x - 5 y = 7

10 - 5 x = 3 (x - 4) - 2 (x + 7)

x = \frac{10 a 0.1}{10}

18000 = (x) \times (1 + 2 \times 20)

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