Solve x^2+(3/2)^2=(9/2-x)^2

$$x ^ { 2 } + ( \frac { 3 } { 2 } ) ^ { 2 } = ( \frac { 9 } { 2 } - x ) ^ { 2 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$x^{2}+\frac{9}{4}=\left(\frac{9}{2}-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{9}{2}-x\right)^{2}.

$$x^{2}+\frac{9}{4}=\frac{81}{4}-9x+x^{2}$$

Add 9x to both sides.

$$x^{2}+\frac{9}{4}+9x=\frac{81}{4}+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+\frac{9}{4}+9x-x^{2}=\frac{81}{4}$$

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

$$\frac{9}{4}+9x=\frac{81}{4}$$

Subtract \frac{9}{4} from both sides.

$$9x=\frac{81}{4}-\frac{9}{4}$$

Subtract \frac{9}{4} from \frac{81}{4} to get 18.

$$9x=18$$

Divide both sides by 9.

$$x=\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$x=2$$