Solve 6x^2-27=0

$$6 { x }^{ 2 } -27=0$$

Solve for x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Steps by Finding Square Root

Add 27 to both sides. Anything plus zero gives itself.

$$6x^{2}=27$$

Divide both sides by 6.

$$x^{2}=\frac{27}{6}$$

Reduce the fraction \frac{27}{6} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{9}{2}$$

Take the square root of both sides of the equation.

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

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.

$$6x^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-27\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-27\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-27\right)}}{2\times 6}$$

Multiply -24 times -27.

$$x=\frac{0±\sqrt{648}}{2\times 6}$$

Take the square root of 648.

$$x=\frac{0±18\sqrt{2}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±18\sqrt{2}}{12}$$

Now solve the equation x=\frac{0±18\sqrt{2}}{12} when ± is plus.

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

Now solve the equation x=\frac{0±18\sqrt{2}}{12} when ± is minus.

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

The equation is now solved.

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