Solve 100x^2-225=+11

$$100 x ^ { 2 } - 225 = + 11$$

Solve for x

$$x = \frac{\sqrt{59}}{5} \approx 1.53622915$$

$$x = -\frac{\sqrt{59}}{5} \approx -1.53622915$$

Steps by Finding Square Root

Add 225 to both sides.

$$100x^{2}=11+225$$

Add 11 and 225 to get 236.

$$100x^{2}=236$$

Divide both sides by 100.

$$x^{2}=\frac{236}{100}$$

Reduce the fraction \frac{236}{100} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{59}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$

Steps Using the Quadratic Formula

Subtract 11 from both sides.

$$100x^{2}-225-11=0$$

Subtract 11 from -225 to get -236.

$$100x^{2}-236=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -236 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-236\right)}}{2\times 100}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-236\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{0±\sqrt{-400\left(-236\right)}}{2\times 100}$$

Multiply -400 times -236.

$$x=\frac{0±\sqrt{94400}}{2\times 100}$$

Take the square root of 94400.

$$x=\frac{0±40\sqrt{59}}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{0±40\sqrt{59}}{200}$$

Now solve the equation x=\frac{0±40\sqrt{59}}{200} when ± is plus.

$$x=\frac{\sqrt{59}}{5}$$

Now solve the equation x=\frac{0±40\sqrt{59}}{200} when ± is minus.

$$x=-\frac{\sqrt{59}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$