Solve 144+left(x-3right)^2=36+left(x-8right)^2

$$144+ { \left(x-3 \right) }^{ 2 } =36+ { \left(x-8 \right) }^{ 2 }$$

Solve for x

$$x = -\frac{53}{10} = -5\frac{3}{10} = -5.3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$144+x^{2}-6x+9=36+\left(x-8\right)^{2}$$

Add 144 and 9 to get 153.

$$153+x^{2}-6x=36+\left(x-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$153+x^{2}-6x=36+x^{2}-16x+64$$

Add 36 and 64 to get 100.

$$153+x^{2}-6x=100+x^{2}-16x$$

Subtract x^{2} from both sides.

$$153+x^{2}-6x-x^{2}=100-16x$$

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

$$153-6x=100-16x$$

Add 16x to both sides.

$$153-6x+16x=100$$

Combine -6x and 16x to get 10x.

$$153+10x=100$$

Subtract 153 from both sides.

$$10x=100-153$$

Subtract 153 from 100 to get -53.

$$10x=-53$$

Divide both sides by 10.

$$x=\frac{-53}{10}$$

Fraction \frac{-53}{10} can be rewritten as -\frac{53}{10} by extracting the negative sign.

$$x=-\frac{53}{10}$$