Solve 22/7*x^2*48=9856

$$\frac{ 22 }{ 7 } \times { x }^{ 2 } \times 48=9856$$

Solve for x

$$x = \frac{14 \sqrt{3}}{3} \approx 8.082903769$$

$$x = -\frac{14 \sqrt{3}}{3} \approx -8.082903769$$

Steps by Finding Square Root

Multiply \frac{22}{7} and 48 to get \frac{1056}{7}.

$$\frac{1056}{7}x^{2}=9856$$

Multiply both sides by \frac{7}{1056}, the reciprocal of \frac{1056}{7}.

$$x^{2}=9856\times \frac{7}{1056}$$

Multiply 9856 and \frac{7}{1056} to get \frac{196}{3}.

$$x^{2}=\frac{196}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{14\sqrt{3}}{3} x=-\frac{14\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Multiply \frac{22}{7} and 48 to get \frac{1056}{7}.

$$\frac{1056}{7}x^{2}=9856$$

Subtract 9856 from both sides.

$$\frac{1056}{7}x^{2}-9856=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1056}{7} for a, 0 for b, and -9856 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1056}{7}\left(-9856\right)}}{2\times \frac{1056}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1056}{7}\left(-9856\right)}}{2\times \frac{1056}{7}}$$

Multiply -4 times \frac{1056}{7}.

$$x=\frac{0±\sqrt{-\frac{4224}{7}\left(-9856\right)}}{2\times \frac{1056}{7}}$$

Multiply -\frac{4224}{7} times -9856.

$$x=\frac{0±\sqrt{5947392}}{2\times \frac{1056}{7}}$$

Take the square root of 5947392.

$$x=\frac{0±1408\sqrt{3}}{2\times \frac{1056}{7}}$$

Multiply 2 times \frac{1056}{7}.

$$x=\frac{0±1408\sqrt{3}}{\frac{2112}{7}}$$

Now solve the equation x=\frac{0±1408\sqrt{3}}{\frac{2112}{7}} when ± is plus.

$$x=\frac{14\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±1408\sqrt{3}}{\frac{2112}{7}} when ± is minus.

$$x=-\frac{14\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{14\sqrt{3}}{3} x=-\frac{14\sqrt{3}}{3}$$