Solve 13x^2-39=0

$$13 x ^ { 2 } - 39 = 0$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 39 to both sides. Anything plus zero gives itself.

$$13x^{2}=39$$

Divide both sides by 13.

$$x^{2}=\frac{39}{13}$$

Divide 39 by 13 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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.

$$13x^{2}-39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-39\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-39\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-39\right)}}{2\times 13}$$

Multiply -52 times -39.

$$x=\frac{0±\sqrt{2028}}{2\times 13}$$

Take the square root of 2028.

$$x=\frac{0±26\sqrt{3}}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±26\sqrt{3}}{26}$$

Now solve the equation x=\frac{0±26\sqrt{3}}{26} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±26\sqrt{3}}{26} when ± is minus.

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

The equation is now solved.

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