Solve (4k)^2-4(6)(k^2-1)=0

$$( 4 k ) ^ { 2 } - 4 ( 6 ) ( k ^ { 2 } - 1 ) = 0$$

Solve for k

$$k=\sqrt{3}\approx 1.732050808$$

$$k=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Expand \left(4k\right)^{2}.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Calculate 4 to the power of 2 and get 16.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Multiply 4 and 6 to get 24.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

Use the distributive property to multiply -24 by k^{2}-1.

$$16k^{2}-24k^{2}+24=0$$

Combine 16k^{2} and -24k^{2} to get -8k^{2}.

$$-8k^{2}+24=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$-8k^{2}=-24$$

Divide both sides by -8.

$$k^{2}=\frac{-24}{-8}$$

Divide -24 by -8 to get 3.

$$k^{2}=3$$

Take the square root of both sides of the equation.

$$k=\sqrt{3} k=-\sqrt{3}$$

Steps Using the Quadratic Formula

Expand \left(4k\right)^{2}.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Calculate 4 to the power of 2 and get 16.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Multiply 4 and 6 to get 24.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

Use the distributive property to multiply -24 by k^{2}-1.

$$16k^{2}-24k^{2}+24=0$$

Combine 16k^{2} and -24k^{2} to get -8k^{2}.

$$-8k^{2}+24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -8 for a, 0 for b, and 24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

Multiply -4 times -8.

$$k=\frac{0±\sqrt{32\times 24}}{2\left(-8\right)}$$

Multiply 32 times 24.

$$k=\frac{0±\sqrt{768}}{2\left(-8\right)}$$

Take the square root of 768.

$$k=\frac{0±16\sqrt{3}}{2\left(-8\right)}$$

Multiply 2 times -8.

$$k=\frac{0±16\sqrt{3}}{-16}$$

Now solve the equation k=\frac{0±16\sqrt{3}}{-16} when ± is plus.

$$k=-\sqrt{3}$$

Now solve the equation k=\frac{0±16\sqrt{3}}{-16} when ± is minus.

$$k=\sqrt{3}$$

The equation is now solved.

$$k=-\sqrt{3} k=\sqrt{3}$$