What is the answer to x^2-12x+a=(x+b)^2 ?

The answer to x^2-12x+a=(x+b)^2 is x=-(b^2-a)/(2(6+b));\quad b\ne-6

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x^2-12x+a=(x+b)^2

x^{2} - 12 x + a = (x + b)^{2}

x = - \frac{b ^{2} - a}{2 ( 6 + b )}; b \neq = - 6

Solution steps

x^{2} - 12 x + a = (x + b)^{2}

Expand

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

x^{2} - 12 x + a = x^{2} + 2 b x + b^{2}

Move

a

to the right side

x^{2} - 12 x = x^{2} + 2 b x + b^{2} - a

Subtract

x^{2} + 2 b x

from both sides

x^{2} - 12 x - (x^{2} + 2 b x) = x^{2} + 2 b x + b^{2} - a - (x^{2} + 2 b x)

Simplify

- 2 b x - 12 x = b^{2} - a

Factor

- 2 b x - 12 x : - 2 x (b + 6)

- 2 x (b + 6) = b^{2} - a

Divide both sides by

- 2 (b + 6); b \neq = - 6

x = - \frac{b ^{2} - a}{2 ( 6 + b )}; b \neq = - 6

\frac{x}{7} = \frac{x - 3}{4}

0.6 (w + 1) = 3 (0.7 w - 0.3)

x, - 5 x - 4 y = 10

1.8 (d + 0.2) = 2.3 d + 0.06

x, 2 x + 3 y = - 2

What is the answer to x^2-12x+a=(x+b)^2 ?
The answer to x^2-12x+a=(x+b)^2 is x=-(b^2-a)/(2(6+b));\quad b\ne-6