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

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

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-5.

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

Use the distributive property to multiply 2 by x-1.

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

Combine -5x and 2x to get -3x.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}-3x-2=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$x^{2}-3x-2-x^{2}=2x+1$$

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

$$-3x-2=2x+1$$

Subtract 2x from both sides.

$$-3x-2-2x=1$$

Combine -3x and -2x to get -5x.

$$-5x-2=1$$

Add 2 to both sides.

$$-5x=1+2$$

Add 1 and 2 to get 3.

$$-5x=3$$

Divide both sides by -5.

$$x=\frac{3}{-5}$$

Fraction \frac{3}{-5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$x=-\frac{3}{5}$$