Solve 4x^2-12=5

$$4 { x }^{ 2 } -12=5$$

Solve for x

$$x = \frac{\sqrt{17}}{2} \approx 2.061552813$$

$$x = -\frac{\sqrt{17}}{2} \approx -2.061552813$$

Steps by Finding Square Root

Add 12 to both sides.

$$4x^{2}=5+12$$

Add 5 and 12 to get 17.

$$4x^{2}=17$$

Divide both sides by 4.

$$x^{2}=\frac{17}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{17}}{2} x=-\frac{\sqrt{17}}{2}$$

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$4x^{2}-12-5=0$$

Subtract 5 from -12 to get -17.

$$4x^{2}-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-17\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-17\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-17\right)}}{2\times 4}$$

Multiply -16 times -17.

$$x=\frac{0±\sqrt{272}}{2\times 4}$$

Take the square root of 272.

$$x=\frac{0±4\sqrt{17}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{17}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{17}}{8} when ± is plus.

$$x=\frac{\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{17}}{8} when ± is minus.

$$x=-\frac{\sqrt{17}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{17}}{2} x=-\frac{\sqrt{17}}{2}$$