Solve (x+4)^2+5=x(x-1)-3

$$( x + 4 ) ^ { 2 } + 5 = x ( x - 1 ) - 3$$

Solve for x

$$x = -\frac{8}{3} = -2\frac{2}{3} \approx -2.666666667$$

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}.

$$x^{2}+8x+16+5=x\left(x-1\right)-3$$

Add 16 and 5 to get 21.

$$x^{2}+8x+21=x\left(x-1\right)-3$$

Use the distributive property to multiply x by x-1.

$$x^{2}+8x+21=x^{2}-x-3$$

Subtract x^{2} from both sides.

$$x^{2}+8x+21-x^{2}=-x-3$$

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

$$8x+21=-x-3$$

Add x to both sides.

$$8x+21+x=-3$$

Combine 8x and x to get 9x.

$$9x+21=-3$$

Subtract 21 from both sides.

$$9x=-3-21$$

Subtract 21 from -3 to get -24.

$$9x=-24$$

Divide both sides by 9.

$$x=\frac{-24}{9}$$

Reduce the fraction \frac{-24}{9} to lowest terms by extracting and canceling out 3.

$$x=-\frac{8}{3}$$