Solve 8+11=10x^2

$$8+11=10 { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{190}}{10} \approx 1.378404875$$

$$x = -\frac{\sqrt{190}}{10} \approx -1.378404875$$

Steps by Finding Square Root

Add 8 and 11 to get 19.

$$19=10x^{2}$$

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

$$10x^{2}=19$$

Divide both sides by 10.

$$x^{2}=\frac{19}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{190}}{10} x=-\frac{\sqrt{190}}{10}$$

Steps Using the Quadratic Formula

Add 8 and 11 to get 19.

$$19=10x^{2}$$

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

$$10x^{2}=19$$

Subtract 19 from both sides.

$$10x^{2}-19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-19\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-19\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-19\right)}}{2\times 10}$$

Multiply -40 times -19.

$$x=\frac{0±\sqrt{760}}{2\times 10}$$

Take the square root of 760.

$$x=\frac{0±2\sqrt{190}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±2\sqrt{190}}{20}$$

Now solve the equation x=\frac{0±2\sqrt{190}}{20} when ± is plus.

$$x=\frac{\sqrt{190}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{190}}{20} when ± is minus.

$$x=-\frac{\sqrt{190}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{190}}{10} x=-\frac{\sqrt{190}}{10}$$