Solve 16x^2-9=14

$$16 x ^ { 2 } - 9 = 14$$

Solve for x

$$x = \frac{\sqrt{23}}{4} \approx 1.198957881$$

$$x = -\frac{\sqrt{23}}{4} \approx -1.198957881$$

Steps by Finding Square Root

Add 9 to both sides.

$$16x^{2}=14+9$$

Add 14 and 9 to get 23.

$$16x^{2}=23$$

Divide both sides by 16.

$$x^{2}=\frac{23}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{23}}{4} x=-\frac{\sqrt{23}}{4}$$

Steps Using the Quadratic Formula

Subtract 14 from both sides.

$$16x^{2}-9-14=0$$

Subtract 14 from -9 to get -23.

$$16x^{2}-23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-23\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-23\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-23\right)}}{2\times 16}$$

Multiply -64 times -23.

$$x=\frac{0±\sqrt{1472}}{2\times 16}$$

Take the square root of 1472.

$$x=\frac{0±8\sqrt{23}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±8\sqrt{23}}{32}$$

Now solve the equation x=\frac{0±8\sqrt{23}}{32} when ± is plus.

$$x=\frac{\sqrt{23}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{23}}{32} when ± is minus.

$$x=-\frac{\sqrt{23}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{23}}{4} x=-\frac{\sqrt{23}}{4}$$