Solve 10x^2+2=9

$$10 x ^ { 2 } + 2 = 9$$

Solve for x

$$x=\frac{\sqrt{70}}{10}\approx 0.836660027$$

$$x=-\frac{\sqrt{70}}{10}\approx -0.836660027$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$10x^{2}=9-2$$

Subtract 2 from 9 to get 7.

$$10x^{2}=7$$

Divide both sides by 10.

$$x^{2}=\frac{7}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{70}}{10} x=-\frac{\sqrt{70}}{10}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$10x^{2}+2-9=0$$

Subtract 9 from 2 to get -7.

$$10x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-7\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-7\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-7\right)}}{2\times 10}$$

Multiply -40 times -7.

$$x=\frac{0±\sqrt{280}}{2\times 10}$$

Take the square root of 280.

$$x=\frac{0±2\sqrt{70}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±2\sqrt{70}}{20}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{20} when ± is plus.

$$x=\frac{\sqrt{70}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{20} when ± is minus.

$$x=-\frac{\sqrt{70}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{70}}{10} x=-\frac{\sqrt{70}}{10}$$