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

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

Solve for x

$$x = \frac{3 \sqrt{5}}{2} \approx 3.354101966$$

$$x = -\frac{3 \sqrt{5}}{2} \approx -3.354101966$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

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

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

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

Add 9 and \frac{9}{4} to get \frac{45}{4}.

$$\frac{45}{4}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{45}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{5}}{2} x=-\frac{3\sqrt{5}}{2}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

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

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

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

Add 9 and \frac{9}{4} to get \frac{45}{4}.

$$\frac{45}{4}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{45}{4}$$

Subtract \frac{45}{4} from both sides.

$$x^{2}-\frac{45}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{45}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{45}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{45}{4}\right)}}{2}$$

Multiply -4 times -\frac{45}{4}.

$$x=\frac{0±\sqrt{45}}{2}$$

Take the square root of 45.

$$x=\frac{0±3\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{5}}{2} when ± is plus.

$$x=\frac{3\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{5}}{2} when ± is minus.

$$x=-\frac{3\sqrt{5}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}}{2} x=-\frac{3\sqrt{5}}{2}$$