Solve x^2=(3/2)^2+(3/5)^2

$$x ^ { 2 } = ( \frac { 3 } { 2 } ) ^ { 2 } + ( \frac { 3 } { 5 } ) ^ { 2 }$$

Solve for x

$$x = \frac{3 \sqrt{29}}{10} \approx 1.615549442$$

$$x = -\frac{3 \sqrt{29}}{10} \approx -1.615549442$$

Steps by Finding Square Root

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

$$x^{2}=\frac{9}{4}+\left(\frac{3}{5}\right)^{2}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$x^{2}=\frac{9}{4}+\frac{9}{25}$$

Add \frac{9}{4} and \frac{9}{25} to get \frac{261}{100}.

$$x^{2}=\frac{261}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{29}}{10} x=-\frac{3\sqrt{29}}{10}$$

Steps Using the Quadratic Formula

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

$$x^{2}=\frac{9}{4}+\left(\frac{3}{5}\right)^{2}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$x^{2}=\frac{9}{4}+\frac{9}{25}$$

Add \frac{9}{4} and \frac{9}{25} to get \frac{261}{100}.

$$x^{2}=\frac{261}{100}$$

Subtract \frac{261}{100} from both sides.

$$x^{2}-\frac{261}{100}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{261}{100} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{261}{100}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{261}{100}\right)}}{2}$$

Multiply -4 times -\frac{261}{100}.

$$x=\frac{0±\sqrt{\frac{261}{25}}}{2}$$

Take the square root of \frac{261}{25}.

$$x=\frac{0±\frac{3\sqrt{29}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{29}}{5}}{2} when ± is plus.

$$x=\frac{3\sqrt{29}}{10}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{29}}{5}}{2} when ± is minus.

$$x=-\frac{3\sqrt{29}}{10}$$

The equation is now solved.

$$x=\frac{3\sqrt{29}}{10} x=-\frac{3\sqrt{29}}{10}$$