Solve 8x^2+3=54

$$8 { x }^{ 2 } +3=54$$

Solve for x

$$x = \frac{\sqrt{102}}{4} \approx 2.524876235$$

$$x = -\frac{\sqrt{102}}{4} \approx -2.524876235$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$8x^{2}=54-3$$

Subtract 3 from 54 to get 51.

$$8x^{2}=51$$

Divide both sides by 8.

$$x^{2}=\frac{51}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{102}}{4} x=-\frac{\sqrt{102}}{4}$$

Steps Using the Quadratic Formula

Subtract 54 from both sides.

$$8x^{2}+3-54=0$$

Subtract 54 from 3 to get -51.

$$8x^{2}-51=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -51 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-51\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-51\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-51\right)}}{2\times 8}$$

Multiply -32 times -51.

$$x=\frac{0±\sqrt{1632}}{2\times 8}$$

Take the square root of 1632.

$$x=\frac{0±4\sqrt{102}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±4\sqrt{102}}{16}$$

Now solve the equation x=\frac{0±4\sqrt{102}}{16} when ± is plus.

$$x=\frac{\sqrt{102}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{102}}{16} when ± is minus.

$$x=-\frac{\sqrt{102}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{102}}{4} x=-\frac{\sqrt{102}}{4}$$