Solve 9x*x+13=69

$$9x \times x+13=69$$

Solve for x

$$x = \frac{2 \sqrt{14}}{3} \approx 2.494438258$$

$$x = -\frac{2 \sqrt{14}}{3} \approx -2.494438258$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$9x^{2}+13=69$$

Subtract 13 from both sides.

$$9x^{2}=69-13$$

Subtract 13 from 69 to get 56.

$$9x^{2}=56$$

Divide both sides by 9.

$$x^{2}=\frac{56}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{14}}{3} x=-\frac{2\sqrt{14}}{3}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$9x^{2}+13=69$$

Subtract 69 from both sides.

$$9x^{2}+13-69=0$$

Subtract 69 from 13 to get -56.

$$9x^{2}-56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-56\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-56\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-56\right)}}{2\times 9}$$

Multiply -36 times -56.

$$x=\frac{0±\sqrt{2016}}{2\times 9}$$

Take the square root of 2016.

$$x=\frac{0±12\sqrt{14}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±12\sqrt{14}}{18}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{18} when ± is plus.

$$x=\frac{2\sqrt{14}}{3}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{18} when ± is minus.

$$x=-\frac{2\sqrt{14}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{14}}{3} x=-\frac{2\sqrt{14}}{3}$$