Solve 3x^2-14=526

$$3 x ^ { 2 } - 14 = 526$$

Solve for x

$$x=6\sqrt{5}\approx 13.416407865$$

$$x=-6\sqrt{5}\approx -13.416407865$$

Steps by Finding Square Root

Add 14 to both sides.

$$3x^{2}=526+14$$

Add 526 and 14 to get 540.

$$3x^{2}=540$$

Divide both sides by 3.

$$x^{2}=\frac{540}{3}$$

Divide 540 by 3 to get 180.

$$x^{2}=180$$

Take the square root of both sides of the equation.

$$x=6\sqrt{5} x=-6\sqrt{5}$$

Steps Using the Quadratic Formula

Subtract 526 from both sides.

$$3x^{2}-14-526=0$$

Subtract 526 from -14 to get -540.

$$3x^{2}-540=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -540 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-540\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-540\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-540\right)}}{2\times 3}$$

Multiply -12 times -540.

$$x=\frac{0±\sqrt{6480}}{2\times 3}$$

Take the square root of 6480.

$$x=\frac{0±36\sqrt{5}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±36\sqrt{5}}{6}$$

Now solve the equation x=\frac{0±36\sqrt{5}}{6} when ± is plus.

$$x=6\sqrt{5}$$

Now solve the equation x=\frac{0±36\sqrt{5}}{6} when ± is minus.

$$x=-6\sqrt{5}$$

The equation is now solved.

$$x=6\sqrt{5} x=-6\sqrt{5}$$