Solve 11x^2-10=67

$$11 { x }^{ 2 } -10=67$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Add 10 to both sides.

$$11x^{2}=67+10$$

Add 67 and 10 to get 77.

$$11x^{2}=77$$

Divide both sides by 11.

$$x^{2}=\frac{77}{11}$$

Divide 77 by 11 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 67 from both sides.

$$11x^{2}-10-67=0$$

Subtract 67 from -10 to get -77.

$$11x^{2}-77=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -77 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-77\right)}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-77\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\left(-77\right)}}{2\times 11}$$

Multiply -44 times -77.

$$x=\frac{0±\sqrt{3388}}{2\times 11}$$

Take the square root of 3388.

$$x=\frac{0±22\sqrt{7}}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±22\sqrt{7}}{22}$$

Now solve the equation x=\frac{0±22\sqrt{7}}{22} when ± is plus.

$$x=\sqrt{7}$$

Now solve the equation x=\frac{0±22\sqrt{7}}{22} when ± is minus.

$$x=-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7} x=-\sqrt{7}$$