Solve 5=100-90x^2

$$5=100-90 { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{38}}{6} \approx 1.027402334$$

$$x = -\frac{\sqrt{38}}{6} \approx -1.027402334$$

Steps by Finding Square Root

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

$$100-90x^{2}=5$$

Subtract 100 from both sides.

$$-90x^{2}=5-100$$

Subtract 100 from 5 to get -95.

$$-90x^{2}=-95$$

Divide both sides by -90.

$$x^{2}=\frac{-95}{-90}$$

Reduce the fraction \frac{-95}{-90} to lowest terms by extracting and canceling out -5.

$$x^{2}=\frac{19}{18}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{38}}{6} x=-\frac{\sqrt{38}}{6}$$

Steps Using the Quadratic Formula

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

$$100-90x^{2}=5$$

Subtract 5 from both sides.

$$100-90x^{2}-5=0$$

Subtract 5 from 100 to get 95.

$$95-90x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-90x^{2}+95=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -90 for a, 0 for b, and 95 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-90\right)\times 95}}{2\left(-90\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-90\right)\times 95}}{2\left(-90\right)}$$

Multiply -4 times -90.

$$x=\frac{0±\sqrt{360\times 95}}{2\left(-90\right)}$$

Multiply 360 times 95.

$$x=\frac{0±\sqrt{34200}}{2\left(-90\right)}$$

Take the square root of 34200.

$$x=\frac{0±30\sqrt{38}}{2\left(-90\right)}$$

Multiply 2 times -90.

$$x=\frac{0±30\sqrt{38}}{-180}$$

Now solve the equation x=\frac{0±30\sqrt{38}}{-180} when ± is plus.

$$x=-\frac{\sqrt{38}}{6}$$

Now solve the equation x=\frac{0±30\sqrt{38}}{-180} when ± is minus.

$$x=\frac{\sqrt{38}}{6}$$

The equation is now solved.

$$x=-\frac{\sqrt{38}}{6} x=\frac{\sqrt{38}}{6}$$