Solve 9x^2+5=44

$$9 { x }^{ 2 } +5=44$$

Solve for x

$$x = \frac{\sqrt{39}}{3} \approx 2.081665999$$

$$x = -\frac{\sqrt{39}}{3} \approx -2.081665999$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$9x^{2}=44-5$$

Subtract 5 from 44 to get 39.

$$9x^{2}=39$$

Divide both sides by 9.

$$x^{2}=\frac{39}{9}$$

Reduce the fraction \frac{39}{9} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{13}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{39}}{3} x=-\frac{\sqrt{39}}{3}$$

Steps Using the Quadratic Formula

Subtract 44 from both sides.

$$9x^{2}+5-44=0$$

Subtract 44 from 5 to get -39.

$$9x^{2}-39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-39\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-39\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-39\right)}}{2\times 9}$$

Multiply -36 times -39.

$$x=\frac{0±\sqrt{1404}}{2\times 9}$$

Take the square root of 1404.

$$x=\frac{0±6\sqrt{39}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{39}}{18}$$

Now solve the equation x=\frac{0±6\sqrt{39}}{18} when ± is plus.

$$x=\frac{\sqrt{39}}{3}$$

Now solve the equation x=\frac{0±6\sqrt{39}}{18} when ± is minus.

$$x=-\frac{\sqrt{39}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{39}}{3} x=-\frac{\sqrt{39}}{3}$$