Solve 22/7*x*x=484

$$\frac{ 22 }{ 7 } \times x \times x=484$$

Solve for x

$$x=\sqrt{154}\approx 12.409673646$$

$$x=-\sqrt{154}\approx -12.409673646$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$\frac{22}{7}x^{2}=484$$

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$x^{2}=484\times \frac{7}{22}$$

Express 484\times \frac{7}{22} as a single fraction.

$$x^{2}=\frac{484\times 7}{22}$$

Multiply 484 and 7 to get 3388.

$$x^{2}=\frac{3388}{22}$$

Divide 3388 by 22 to get 154.

$$x^{2}=154$$

Take the square root of both sides of the equation.

$$x=\sqrt{154} x=-\sqrt{154}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$\frac{22}{7}x^{2}=484$$

Subtract 484 from both sides.

$$\frac{22}{7}x^{2}-484=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{22}{7} for a, 0 for b, and -484 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{22}{7}\left(-484\right)}}{2\times \frac{22}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{22}{7}\left(-484\right)}}{2\times \frac{22}{7}}$$

Multiply -4 times \frac{22}{7}.

$$x=\frac{0±\sqrt{-\frac{88}{7}\left(-484\right)}}{2\times \frac{22}{7}}$$

Multiply -\frac{88}{7} times -484.

$$x=\frac{0±\sqrt{\frac{42592}{7}}}{2\times \frac{22}{7}}$$

Take the square root of \frac{42592}{7}.

$$x=\frac{0±\frac{44\sqrt{154}}{7}}{2\times \frac{22}{7}}$$

Multiply 2 times \frac{22}{7}.

$$x=\frac{0±\frac{44\sqrt{154}}{7}}{\frac{44}{7}}$$

Now solve the equation x=\frac{0±\frac{44\sqrt{154}}{7}}{\frac{44}{7}} when ± is plus.

$$x=\sqrt{154}$$

Now solve the equation x=\frac{0±\frac{44\sqrt{154}}{7}}{\frac{44}{7}} when ± is minus.

$$x=-\sqrt{154}$$

The equation is now solved.

$$x=\sqrt{154} x=-\sqrt{154}$$