Solve 770=200/300*22/7*x^2

$$770= \frac{ 200 }{ 300 } \times \frac{ 22 }{ 7 } \times { x }^{ 2 }$$

Solve for x

$$x = \frac{7 \sqrt{30}}{2} \approx 19.170289513$$

$$x = -\frac{7 \sqrt{30}}{2} \approx -19.170289513$$

Steps by Finding Square Root

Reduce the fraction \frac{200}{300} to lowest terms by extracting and canceling out 100.

$$770=\frac{2}{3}\times \frac{22}{7}x^{2}$$

Multiply \frac{2}{3} and \frac{22}{7} to get \frac{44}{21}.

$$770=\frac{44}{21}x^{2}$$

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

$$\frac{44}{21}x^{2}=770$$

Multiply both sides by \frac{21}{44}, the reciprocal of \frac{44}{21}.

$$x^{2}=770\times \frac{21}{44}$$

Multiply 770 and \frac{21}{44} to get \frac{735}{2}.

$$x^{2}=\frac{735}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{30}}{2} x=-\frac{7\sqrt{30}}{2}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{200}{300} to lowest terms by extracting and canceling out 100.

$$770=\frac{2}{3}\times \frac{22}{7}x^{2}$$

Multiply \frac{2}{3} and \frac{22}{7} to get \frac{44}{21}.

$$770=\frac{44}{21}x^{2}$$

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

$$\frac{44}{21}x^{2}=770$$

Subtract 770 from both sides.

$$\frac{44}{21}x^{2}-770=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{44}{21} for a, 0 for b, and -770 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{44}{21}\left(-770\right)}}{2\times \frac{44}{21}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{44}{21}\left(-770\right)}}{2\times \frac{44}{21}}$$

Multiply -4 times \frac{44}{21}.

$$x=\frac{0±\sqrt{-\frac{176}{21}\left(-770\right)}}{2\times \frac{44}{21}}$$

Multiply -\frac{176}{21} times -770.

$$x=\frac{0±\sqrt{\frac{19360}{3}}}{2\times \frac{44}{21}}$$

Take the square root of \frac{19360}{3}.

$$x=\frac{0±\frac{44\sqrt{30}}{3}}{2\times \frac{44}{21}}$$

Multiply 2 times \frac{44}{21}.

$$x=\frac{0±\frac{44\sqrt{30}}{3}}{\frac{88}{21}}$$

Now solve the equation x=\frac{0±\frac{44\sqrt{30}}{3}}{\frac{88}{21}} when ± is plus.

$$x=\frac{7\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±\frac{44\sqrt{30}}{3}}{\frac{88}{21}} when ± is minus.

$$x=-\frac{7\sqrt{30}}{2}$$

The equation is now solved.

$$x=\frac{7\sqrt{30}}{2} x=-\frac{7\sqrt{30}}{2}$$