Solve 11=41-4*9x^2

$$11 = 41 - 4 \cdot 9 x ^ { 2 }$$

Solve for x

$$x=\frac{\sqrt{30}}{6}\approx 0.912870929$$

$$x=-\frac{\sqrt{30}}{6}\approx -0.912870929$$

Steps by Finding Square Root

Multiply 4 and 9 to get 36.

$$11=41-36x^{2}$$

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

$$41-36x^{2}=11$$

Subtract 41 from both sides.

$$-36x^{2}=11-41$$

Subtract 41 from 11 to get -30.

$$-36x^{2}=-30$$

Divide both sides by -36.

$$x^{2}=\frac{-30}{-36}$$

Reduce the fraction \frac{-30}{-36} to lowest terms by extracting and canceling out -6.

$$x^{2}=\frac{5}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{6} x=-\frac{\sqrt{30}}{6}$$

Steps Using the Quadratic Formula

Multiply 4 and 9 to get 36.

$$11=41-36x^{2}$$

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

$$41-36x^{2}=11$$

Subtract 11 from both sides.

$$41-36x^{2}-11=0$$

Subtract 11 from 41 to get 30.

$$30-36x^{2}=0$$

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.

$$-36x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -36 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)\times 30}}{2\left(-36\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)\times 30}}{2\left(-36\right)}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144\times 30}}{2\left(-36\right)}$$

Multiply 144 times 30.

$$x=\frac{0±\sqrt{4320}}{2\left(-36\right)}$$

Take the square root of 4320.

$$x=\frac{0±12\sqrt{30}}{2\left(-36\right)}$$

Multiply 2 times -36.

$$x=\frac{0±12\sqrt{30}}{-72}$$

Now solve the equation x=\frac{0±12\sqrt{30}}{-72} when ± is plus.

$$x=-\frac{\sqrt{30}}{6}$$

Now solve the equation x=\frac{0±12\sqrt{30}}{-72} when ± is minus.

$$x=\frac{\sqrt{30}}{6}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}}{6} x=\frac{\sqrt{30}}{6}$$