Solve x^2=sqrt{100}-.15

$${ x }^{ 2 } = \sqrt{ 100 } -.15$$

Solve for x

$$x = \frac{\sqrt{985}}{10} \approx 3.138470965$$

$$x = -\frac{\sqrt{985}}{10} \approx -3.138470965$$

Steps by Finding Square Root

Calculate the square root of 100 and get 10.

$$x^{2}=10-0.15$$

Subtract 0.15 from 10 to get 9.85.

$$x^{2}=9.85$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{985}}{10} x=-\frac{\sqrt{985}}{10}$$

Steps Using the Quadratic Formula

Calculate the square root of 100 and get 10.

$$x^{2}=10-0.15$$

Subtract 0.15 from 10 to get 9.85.

$$x^{2}=9.85$$

Subtract 9.85 from both sides.

$$x^{2}-9.85=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9.85 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9.85\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9.85\right)}}{2}$$

Multiply -4 times -9.85.

$$x=\frac{0±\sqrt{39.4}}{2}$$

Take the square root of 39.4.

$$x=\frac{0±\frac{\sqrt{985}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{985}}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{985}}{10}$$

Now solve the equation x=\frac{0±\frac{\sqrt{985}}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{985}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{985}}{10} x=-\frac{\sqrt{985}}{10}$$