Solve (x+4)^2=x(x-14)+5

$$( x + 4 ) ^ { 2 } = x ( x - 14 ) + 5$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16=x\left(x-14\right)+5$$

Use the distributive property to multiply x by x-14.

$$x^{2}+8x+16=x^{2}-14x+5$$

Subtract x^{2} from both sides.

$$x^{2}+8x+16-x^{2}=-14x+5$$

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

$$8x+16=-14x+5$$

Add 14x to both sides.

$$8x+16+14x=5$$

Combine 8x and 14x to get 22x.

$$22x+16=5$$

Subtract 16 from both sides.

$$22x=5-16$$

Subtract 16 from 5 to get -11.

$$22x=-11$$

Divide both sides by 22.

$$x=\frac{-11}{22}$$

Reduce the fraction \frac{-11}{22} to lowest terms by extracting and canceling out 11.

$$x=-\frac{1}{2}$$