Solve 88704=22/7*x^2*36

$$88704= \frac{ 22 }{ 7 } \times { x }^{ 2 } \times 36$$

Solve for x

$$x=28$$

$$x=-28$$

Steps Using Difference of Squares

Multiply \frac{22}{7} and 36 to get \frac{792}{7}.

$$88704=\frac{792}{7}x^{2}$$

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

$$\frac{792}{7}x^{2}=88704$$

Subtract 88704 from both sides.

$$\frac{792}{7}x^{2}-88704=0$$

Divide both sides by \frac{792}{7}.

$$x^{2}-784=0$$

Consider x^{2}-784. Rewrite x^{2}-784 as x^{2}-28^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-28\right)\left(x+28\right)=0$$

To find equation solutions, solve x-28=0 and x+28=0.

$$x=28 x=-28$$

Steps by Finding Square Root

Multiply \frac{22}{7} and 36 to get \frac{792}{7}.

$$88704=\frac{792}{7}x^{2}$$

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

$$\frac{792}{7}x^{2}=88704$$

Multiply both sides by \frac{7}{792}, the reciprocal of \frac{792}{7}.

$$x^{2}=88704\times \frac{7}{792}$$

Multiply 88704 and \frac{7}{792} to get 784.

$$x^{2}=784$$

Take the square root of both sides of the equation.

$$x=28 x=-28$$

Steps Using the Quadratic Formula

Multiply \frac{22}{7} and 36 to get \frac{792}{7}.

$$88704=\frac{792}{7}x^{2}$$

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

$$\frac{792}{7}x^{2}=88704$$

Subtract 88704 from both sides.

$$\frac{792}{7}x^{2}-88704=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{792}{7} for a, 0 for b, and -88704 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{792}{7}\left(-88704\right)}}{2\times \frac{792}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{792}{7}\left(-88704\right)}}{2\times \frac{792}{7}}$$

Multiply -4 times \frac{792}{7}.

$$x=\frac{0±\sqrt{-\frac{3168}{7}\left(-88704\right)}}{2\times \frac{792}{7}}$$

Multiply -\frac{3168}{7} times -88704.

$$x=\frac{0±\sqrt{40144896}}{2\times \frac{792}{7}}$$

Take the square root of 40144896.

$$x=\frac{0±6336}{2\times \frac{792}{7}}$$

Multiply 2 times \frac{792}{7}.

$$x=\frac{0±6336}{\frac{1584}{7}}$$

Now solve the equation x=\frac{0±6336}{\frac{1584}{7}} when ± is plus. Divide 6336 by \frac{1584}{7} by multiplying 6336 by the reciprocal of \frac{1584}{7}.

$$x=28$$

Now solve the equation x=\frac{0±6336}{\frac{1584}{7}} when ± is minus. Divide -6336 by \frac{1584}{7} by multiplying -6336 by the reciprocal of \frac{1584}{7}.

$$x=-28$$

The equation is now solved.

$$x=28 x=-28$$