Solve 113a^2-1239=0

$$113 a ^ { 2 } - 1239 = 0$$

Solve for a

$$a = \frac{\sqrt{140007}}{113} \approx 3.311284006$$

$$a = -\frac{\sqrt{140007}}{113} \approx -3.311284006$$

Steps by Finding Square Root

Add 1239 to both sides. Anything plus zero gives itself.

$$113a^{2}=1239$$

Divide both sides by 113.

$$a^{2}=\frac{1239}{113}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{140007}}{113} a=-\frac{\sqrt{140007}}{113}$$

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.

$$113a^{2}-1239=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 113 for a, 0 for b, and -1239 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 113\left(-1239\right)}}{2\times 113}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 113\left(-1239\right)}}{2\times 113}$$

Multiply -4 times 113.

$$a=\frac{0±\sqrt{-452\left(-1239\right)}}{2\times 113}$$

Multiply -452 times -1239.

$$a=\frac{0±\sqrt{560028}}{2\times 113}$$

Take the square root of 560028.

$$a=\frac{0±2\sqrt{140007}}{2\times 113}$$

Multiply 2 times 113.

$$a=\frac{0±2\sqrt{140007}}{226}$$

Now solve the equation a=\frac{0±2\sqrt{140007}}{226} when ± is plus.

$$a=\frac{\sqrt{140007}}{113}$$

Now solve the equation a=\frac{0±2\sqrt{140007}}{226} when ± is minus.

$$a=-\frac{\sqrt{140007}}{113}$$

The equation is now solved.

$$a=\frac{\sqrt{140007}}{113} a=-\frac{\sqrt{140007}}{113}$$