Solve 9.6+3.23=33v^2/56

$$9.6 + 3.23 = \frac { 33 v ^ { 2 } } { 56 }$$

Solve for v

$$v = \frac{\sqrt{592746}}{165} \approx 4.666060567$$

$$v = -\frac{\sqrt{592746}}{165} \approx -4.666060567$$

Steps by Finding Square Root

Multiply both sides of the equation by 56.

$$537.6+180.88=33v^{2}$$

Add 537.6 and 180.88 to get 718.48.

$$718.48=33v^{2}$$

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

$$33v^{2}=718.48$$

Divide both sides by 33.

$$v^{2}=\frac{718.48}{33}$$

Expand \frac{718.48}{33} by multiplying both numerator and the denominator by 100.

$$v^{2}=\frac{71848}{3300}$$

Reduce the fraction \frac{71848}{3300} to lowest terms by extracting and canceling out 4.

$$v^{2}=\frac{17962}{825}$$

Take the square root of both sides of the equation.

$$v=\frac{\sqrt{592746}}{165} v=-\frac{\sqrt{592746}}{165}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 56.

$$537.6+180.88=33v^{2}$$

Add 537.6 and 180.88 to get 718.48.

$$718.48=33v^{2}$$

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

$$33v^{2}=718.48$$

Subtract 718.48 from both sides.

$$33v^{2}-718.48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 33 for a, 0 for b, and -718.48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 33\left(-718.48\right)}}{2\times 33}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 33\left(-718.48\right)}}{2\times 33}$$

Multiply -4 times 33.

$$v=\frac{0±\sqrt{-132\left(-718.48\right)}}{2\times 33}$$

Multiply -132 times -718.48.

$$v=\frac{0±\sqrt{94839.36}}{2\times 33}$$

Take the square root of 94839.36.

$$v=\frac{0±\frac{2\sqrt{592746}}{5}}{2\times 33}$$

Multiply 2 times 33.

$$v=\frac{0±\frac{2\sqrt{592746}}{5}}{66}$$

Now solve the equation v=\frac{0±\frac{2\sqrt{592746}}{5}}{66} when ± is plus.

$$v=\frac{\sqrt{592746}}{165}$$

Now solve the equation v=\frac{0±\frac{2\sqrt{592746}}{5}}{66} when ± is minus.

$$v=-\frac{\sqrt{592746}}{165}$$

The equation is now solved.

$$v=\frac{\sqrt{592746}}{165} v=-\frac{\sqrt{592746}}{165}$$