Solve (x+3)^2=x(x-2)

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

Solve for x

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$$

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}.

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

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

$$x^{2}+6x+9=x^{2}-2x$$

Subtract x^{2} from both sides.

$$x^{2}+6x+9-x^{2}=-2x$$

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

$$6x+9=-2x$$

Add 2x to both sides.

$$6x+9+2x=0$$

Combine 6x and 2x to get 8x.

$$8x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$8x=-9$$

Divide both sides by 8.

$$x=\frac{-9}{8}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$x=-\frac{9}{8}$$