Solve 26500=118x^2+660+3648

$$26500 = 118 x ^ { 2 } + 660 + 3648$$

Solve for x

$$x = \frac{2 \sqrt{163666}}{59} \approx 13.713781266$$

$$x = -\frac{2 \sqrt{163666}}{59} \approx -13.713781266$$

Steps by Finding Square Root

Add 660 and 3648 to get 4308.

$$26500=118x^{2}+4308$$

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

$$118x^{2}+4308=26500$$

Subtract 4308 from both sides.

$$118x^{2}=26500-4308$$

Subtract 4308 from 26500 to get 22192.

$$118x^{2}=22192$$

Divide both sides by 118.

$$x^{2}=\frac{22192}{118}$$

Reduce the fraction \frac{22192}{118} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{11096}{59}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{163666}}{59} x=-\frac{2\sqrt{163666}}{59}$$

Steps Using the Quadratic Formula

Add 660 and 3648 to get 4308.

$$26500=118x^{2}+4308$$

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

$$118x^{2}+4308=26500$$

Subtract 26500 from both sides.

$$118x^{2}[phone]=0$$

Subtract 26500 from 4308 to get -22192.

$$118x^{2}-22192=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 118 for a, 0 for b, and -22192 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 118\left(-22192\right)}}{2\times 118}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 118\left(-22192\right)}}{2\times 118}$$

Multiply -4 times 118.

$$x=\frac{0±\sqrt{-472\left(-22192\right)}}{2\times 118}$$

Multiply -472 times -22192.

$$x=\frac{0±\sqrt{10474624}}{2\times 118}$$

Take the square root of 10474624.

$$x=\frac{0±8\sqrt{163666}}{2\times 118}$$

Multiply 2 times 118.

$$x=\frac{0±8\sqrt{163666}}{236}$$

Now solve the equation x=\frac{0±8\sqrt{163666}}{236} when ± is plus.

$$x=\frac{2\sqrt{163666}}{59}$$

Now solve the equation x=\frac{0±8\sqrt{163666}}{236} when ± is minus.

$$x=-\frac{2\sqrt{163666}}{59}$$

The equation is now solved.

$$x=\frac{2\sqrt{163666}}{59} x=-\frac{2\sqrt{163666}}{59}$$