Solve 4^2x^2=60

$${ 4 }^{ 2 } { x }^{ 2 } =60$$

Solve for x

$$x = \frac{\sqrt{15}}{2} \approx 1.936491673$$

$$x = -\frac{\sqrt{15}}{2} \approx -1.936491673$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=60$$

Divide both sides by 16.

$$x^{2}=\frac{60}{16}$$

Reduce the fraction \frac{60}{16} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{15}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{2} x=-\frac{\sqrt{15}}{2}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=60$$

Subtract 60 from both sides.

$$16x^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-60\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-60\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-60\right)}}{2\times 16}$$

Multiply -64 times -60.

$$x=\frac{0±\sqrt{3840}}{2\times 16}$$

Take the square root of 3840.

$$x=\frac{0±16\sqrt{15}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±16\sqrt{15}}{32}$$

Now solve the equation x=\frac{0±16\sqrt{15}}{32} when ± is plus.

$$x=\frac{\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{15}}{32} when ± is minus.

$$x=-\frac{\sqrt{15}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{2} x=-\frac{\sqrt{15}}{2}$$