Solve 33=u^2/5

$$33 = \frac { u ^ { 2 } } { 5 }$$

Solve for u

$$u=\sqrt{165}\approx 12.845232579$$

$$u=-\sqrt{165}\approx -12.845232579$$

Steps by Finding Square Root

Multiply both sides by 5.

$$33\times 5=u^{2}$$

Multiply 33 and 5 to get 165.

$$165=u^{2}$$

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

$$u^{2}=165$$

Take the square root of both sides of the equation.

$$u=\sqrt{165} u=-\sqrt{165}$$

Steps Using the Quadratic Formula

Multiply both sides by 5.

$$33\times 5=u^{2}$$

Multiply 33 and 5 to get 165.

$$165=u^{2}$$

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

$$u^{2}=165$$

Subtract 165 from both sides.

$$u^{2}-165=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -165 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{0±\sqrt{0^{2}-4\left(-165\right)}}{2}$$

Square 0.

$$u=\frac{0±\sqrt{-4\left(-165\right)}}{2}$$

Multiply -4 times -165.

$$u=\frac{0±\sqrt{660}}{2}$$

Take the square root of 660.

$$u=\frac{0±2\sqrt{165}}{2}$$

Now solve the equation u=\frac{0±2\sqrt{165}}{2} when ± is plus.

$$u=\sqrt{165}$$

Now solve the equation u=\frac{0±2\sqrt{165}}{2} when ± is minus.

$$u=-\sqrt{165}$$

The equation is now solved.

$$u=\sqrt{165} u=-\sqrt{165}$$