Solve 22/7x^28=308

$$\frac{ 22 }{ 7 } { x }^{ 2 } 8 = 308$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps Using Difference of Squares

Multiply \frac{22}{7} and 8 to get \frac{176}{7}.

$$\frac{176}{7}x^{2}=308$$

Subtract 308 from both sides.

$$\frac{176}{7}x^{2}-308=0$$

Divide both sides by \frac{44}{7}.

$$4x^{2}-49=0$$

Consider 4x^{2}-49. Rewrite 4x^{2}-49 as \left(2x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-7\right)\left(2x+7\right)=0$$

To find equation solutions, solve 2x-7=0 and 2x+7=0.

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

Steps by Finding Square Root

Multiply \frac{22}{7} and 8 to get \frac{176}{7}.

$$\frac{176}{7}x^{2}=308$$

Multiply both sides by \frac{7}{176}, the reciprocal of \frac{176}{7}.

$$x^{2}=308\times \frac{7}{176}$$

Multiply 308 and \frac{7}{176} to get \frac{49}{4}.

$$x^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply \frac{22}{7} and 8 to get \frac{176}{7}.

$$\frac{176}{7}x^{2}=308$$

Subtract 308 from both sides.

$$\frac{176}{7}x^{2}-308=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{176}{7} for a, 0 for b, and -308 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{176}{7}\left(-308\right)}}{2\times \frac{176}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{176}{7}\left(-308\right)}}{2\times \frac{176}{7}}$$

Multiply -4 times \frac{176}{7}.

$$x=\frac{0±\sqrt{-\frac{704}{7}\left(-308\right)}}{2\times \frac{176}{7}}$$

Multiply -\frac{704}{7} times -308.

$$x=\frac{0±\sqrt{30976}}{2\times \frac{176}{7}}$$

Take the square root of 30976.

$$x=\frac{0±176}{2\times \frac{176}{7}}$$

Multiply 2 times \frac{176}{7}.

$$x=\frac{0±176}{\frac{352}{7}}$$

Now solve the equation x=\frac{0±176}{\frac{352}{7}} when ± is plus. Divide 176 by \frac{352}{7} by multiplying 176 by the reciprocal of \frac{352}{7}.

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

Now solve the equation x=\frac{0±176}{\frac{352}{7}} when ± is minus. Divide -176 by \frac{352}{7} by multiplying -176 by the reciprocal of \frac{352}{7}.

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

The equation is now solved.

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