What is the answer to (x+a)^2=x^2+22x+b ?

The answer to (x+a)^2=x^2+22x+b is x=(b-a^2)/(2(-11+a));\quad a\ne 11

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(x+a)^2=x^2+22x+b

(x + a)^{2} = x^{2} + 22 x + b

x = \frac{b - a ^{2}}{2 ( - 11 + a )}; a \neq = 11

Solution steps

(x + a)^{2} = x^{2} + 22 x + b

Expand

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

x^{2} + 2 a x + a^{2} = x^{2} + 22 x + b

Move

a^{2}

to the right side

x^{2} + 2 a x = x^{2} + 22 x + b - a^{2}

Subtract

x^{2} + 22 x

from both sides

x^{2} + 2 a x - (x^{2} + 22 x) = x^{2} + 22 x + b - a^{2} - (x^{2} + 22 x)

Simplify

2 a x - 22 x = b - a^{2}

Factor

2 a x - 22 x : 2 x (a - 11)

2 x (a - 11) = b - a^{2}

Divide both sides by

2 (a - 11); a \neq = 11

x = \frac{b - a ^{2}}{2 ( - 11 + a )}; a \neq = 11

- 5 (6 - 3 g) = 7 g + 18

x, \frac{1}{3} x + \frac{1}{2} y = 4

x, y + x = - 2

x = 1 + \frac{1}{2} + \frac{1}{1}

38 x - 72 = 2 x - 216

What is the answer to (x+a)^2=x^2+22x+b ?
The answer to (x+a)^2=x^2+22x+b is x=(b-a^2)/(2(-11+a));\quad a\ne 11