Solve 52-9x^2=24

$$52 - 9 x ^ { 2 } = 24$$

Solve for x

$$x = \frac{2 \sqrt{7}}{3} \approx 1.763834207$$

$$x = -\frac{2 \sqrt{7}}{3} \approx -1.763834207$$

Steps by Finding Square Root

Subtract 52 from both sides.

$$-9x^{2}=24-52$$

Subtract 52 from 24 to get -28.

$$-9x^{2}=-28$$

Divide both sides by -9.

$$x^{2}=\frac{-28}{-9}$$

Fraction \frac{-28}{-9} can be simplified to \frac{28}{9} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{28}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{7}}{3} x=-\frac{2\sqrt{7}}{3}$$

Steps Using the Quadratic Formula

Subtract 24 from both sides.

$$52-9x^{2}-24=0$$

Subtract 24 from 52 to get 28.

$$28-9x^{2}=0$$

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.

$$-9x^{2}+28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 28}}{2\left(-9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 28}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 28}}{2\left(-9\right)}$$

Multiply 36 times 28.

$$x=\frac{0±\sqrt{1008}}{2\left(-9\right)}$$

Take the square root of 1008.

$$x=\frac{0±12\sqrt{7}}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±12\sqrt{7}}{-18}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-18} when ± is plus.

$$x=-\frac{2\sqrt{7}}{3}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-18} when ± is minus.

$$x=\frac{2\sqrt{7}}{3}$$

The equation is now solved.

$$x=-\frac{2\sqrt{7}}{3} x=\frac{2\sqrt{7}}{3}$$