Solve x^2-12x+1=left(x-6right)^2-35

$${ x }^{ 2 } -12x+1= { \left(x-6 \right) }^{ 2 } -35$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+1=x^{2}-12x+36-35$$

Subtract 35 from 36 to get 1.

$$x^{2}-12x+1=x^{2}-12x+1$$

Subtract x^{2} from both sides.

$$x^{2}-12x+1-x^{2}=-12x+1$$

Combine x^{2} and -x^{2} to get 0.

$$-12x+1=-12x+1$$

Add 12x to both sides.

$$-12x+1+12x=1$$

Combine -12x and 12x to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+1=x^{2}-12x+36-35$$

Subtract 35 from 36 to get 1.

$$x^{2}-12x+1=x^{2}-12x+1$$

Subtract x^{2} from both sides.

$$x^{2}-12x+1-x^{2}=-12x+1$$

Combine x^{2} and -x^{2} to get 0.

$$-12x+1=-12x+1$$

Add 12x to both sides.

$$-12x+1+12x=1$$

Combine -12x and 12x to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$