Solve 26252x^2-3=0

$$26252 { x }^{ 2 } -3=0$$

Solve for x

$$x=\frac{\sqrt{19689}}{13126}\approx 0.010690042$$

$$x=-\frac{\sqrt{19689}}{13126}\approx -0.010690042$$

Steps by Finding Square Root

Add 3 to both sides. Anything plus zero gives itself.

$$26252x^{2}=3$$

Divide both sides by 26252.

$$x^{2}=\frac{3}{26252}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{19689}}{13126} x=-\frac{\sqrt{19689}}{13126}$$

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.

$$26252x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26252 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 26252\left(-3\right)}}{2\times 26252}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 26252\left(-3\right)}}{2\times 26252}$$

Multiply -4 times 26252.

$$x=\frac{0±\sqrt{-105008\left(-3\right)}}{2\times 26252}$$

Multiply -105008 times -3.

$$x=\frac{0±\sqrt{315024}}{2\times 26252}$$

Take the square root of 315024.

$$x=\frac{0±4\sqrt{19689}}{2\times 26252}$$

Multiply 2 times 26252.

$$x=\frac{0±4\sqrt{19689}}{52504}$$

Now solve the equation x=\frac{0±4\sqrt{19689}}{52504} when ± is plus.

$$x=\frac{\sqrt{19689}}{13126}$$

Now solve the equation x=\frac{0±4\sqrt{19689}}{52504} when ± is minus.

$$x=-\frac{\sqrt{19689}}{13126}$$

The equation is now solved.

$$x=\frac{\sqrt{19689}}{13126} x=-\frac{\sqrt{19689}}{13126}$$