Solve 8x^2-63=0

$$8 { x }^{ 2 } -63 = 0$$

Solve for x

$$x = \frac{3 \sqrt{14}}{4} \approx 2.80624304$$

$$x = -\frac{3 \sqrt{14}}{4} \approx -2.80624304$$

Steps by Finding Square Root

Add 63 to both sides. Anything plus zero gives itself.

$$8x^{2}=63$$

Divide both sides by 8.

$$x^{2}=\frac{63}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{14}}{4} x=-\frac{3\sqrt{14}}{4}$$

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.

$$8x^{2}-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-63\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-63\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-63\right)}}{2\times 8}$$

Multiply -32 times -63.

$$x=\frac{0±\sqrt{2016}}{2\times 8}$$

Take the square root of 2016.

$$x=\frac{0±12\sqrt{14}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±12\sqrt{14}}{16}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{16} when ± is plus.

$$x=\frac{3\sqrt{14}}{4}$$

Now solve the equation x=\frac{0±12\sqrt{14}}{16} when ± is minus.

$$x=-\frac{3\sqrt{14}}{4}$$

The equation is now solved.

$$x=\frac{3\sqrt{14}}{4} x=-\frac{3\sqrt{14}}{4}$$