Solve 12.13x^2-39=0

$$12.13 x ^ { 2 } - 39 = 0$$

Solve for x

$$x = \frac{10 \sqrt{47307}}{1213} \approx 1.793089234$$

$$x = -\frac{10 \sqrt{47307}}{1213} \approx -1.793089234$$

Steps by Finding Square Root

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

$$12.13x^{2}=39$$

Divide both sides by 12.13.

$$x^{2}=\frac{39}{12.13}$$

Expand \frac{39}{12.13} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{3900}{1213}$$

Take the square root of both sides of the equation.

$$x=\frac{10\sqrt{47307}}{1213} x=-\frac{10\sqrt{47307}}{1213}$$

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.

$$12.13x^{2}-39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12.13 for a, 0 for b, and -39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12.13\left(-39\right)}}{2\times 12.13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12.13\left(-39\right)}}{2\times 12.13}$$

Multiply -4 times 12.13.

$$x=\frac{0±\sqrt{-48.52\left(-39\right)}}{2\times 12.13}$$

Multiply -48.52 times -39.

$$x=\frac{0±\sqrt{1892.28}}{2\times 12.13}$$

Take the square root of 1892.28.

$$x=\frac{0±\frac{\sqrt{47307}}{5}}{2\times 12.13}$$

Multiply 2 times 12.13.

$$x=\frac{0±\frac{\sqrt{47307}}{5}}{24.26}$$

Now solve the equation x=\frac{0±\frac{\sqrt{47307}}{5}}{24.26} when ± is plus.

$$x=\frac{10\sqrt{47307}}{1213}$$

Now solve the equation x=\frac{0±\frac{\sqrt{47307}}{5}}{24.26} when ± is minus.

$$x=-\frac{10\sqrt{47307}}{1213}$$

The equation is now solved.

$$x=\frac{10\sqrt{47307}}{1213} x=-\frac{10\sqrt{47307}}{1213}$$