Solve 6.3x^2-27=0

$$6.3 x ^ { 2 } - 27 = 0$$

Solve for x

$$x = \frac{\sqrt{210}}{7} \approx 2.070196678$$

$$x = -\frac{\sqrt{210}}{7} \approx -2.070196678$$

Steps by Finding Square Root

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

$$6.3x^{2}=27$$

Divide both sides by 6.3.

$$x^{2}=\frac{27}{6.3}$$

Expand \frac{27}{6.3} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{270}{63}$$

Reduce the fraction \frac{270}{63} to lowest terms by extracting and canceling out 9.

$$x^{2}=\frac{30}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{210}}{7} x=-\frac{\sqrt{210}}{7}$$

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.

$$6.3x^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6.3 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6.3\left(-27\right)}}{2\times 6.3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6.3\left(-27\right)}}{2\times 6.3}$$

Multiply -4 times 6.3.

$$x=\frac{0±\sqrt{-25.2\left(-27\right)}}{2\times 6.3}$$

Multiply -25.2 times -27.

$$x=\frac{0±\sqrt{680.4}}{2\times 6.3}$$

Take the square root of 680.4.

$$x=\frac{0±\frac{9\sqrt{210}}{5}}{2\times 6.3}$$

Multiply 2 times 6.3.

$$x=\frac{0±\frac{9\sqrt{210}}{5}}{12.6}$$

Now solve the equation x=\frac{0±\frac{9\sqrt{210}}{5}}{12.6} when ± is plus.

$$x=\frac{\sqrt{210}}{7}$$

Now solve the equation x=\frac{0±\frac{9\sqrt{210}}{5}}{12.6} when ± is minus.

$$x=-\frac{\sqrt{210}}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{210}}{7} x=-\frac{\sqrt{210}}{7}$$