Solve 312-26x^2=0

$$312 - 26 x ^ { 2 } = 0$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

Subtract 312 from both sides. Anything subtracted from zero gives its negation.

$$-26x^{2}=-312$$

Divide both sides by -26.

$$x^{2}=\frac{-312}{-26}$$

Divide -312 by -26 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

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

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.

$$-26x^{2}+312=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -26 for a, 0 for b, and 312 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-26\right)\times 312}}{2\left(-26\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-26\right)\times 312}}{2\left(-26\right)}$$

Multiply -4 times -26.

$$x=\frac{0±\sqrt{104\times 312}}{2\left(-26\right)}$$

Multiply 104 times 312.

$$x=\frac{0±\sqrt{32448}}{2\left(-26\right)}$$

Take the square root of 32448.

$$x=\frac{0±104\sqrt{3}}{2\left(-26\right)}$$

Multiply 2 times -26.

$$x=\frac{0±104\sqrt{3}}{-52}$$

Now solve the equation x=\frac{0±104\sqrt{3}}{-52} when ± is plus.

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

Now solve the equation x=\frac{0±104\sqrt{3}}{-52} when ± is minus.

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

The equation is now solved.

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