Solve 16k^2-144=0

$$16 k ^ { 2 } - 144 = 0$$

Solve for k

$$k=3$$

$$k=-3$$

Steps Using Difference of Squares

Divide both sides by 16.

$$k^{2}-9=0$$

Consider k^{2}-9. Rewrite k^{2}-9 as k^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(k-3\right)\left(k+3\right)=0$$

To find equation solutions, solve k-3=0 and k+3=0.

$$k=3 k=-3$$

Steps by Finding Square Root

Add 144 to both sides. Anything plus zero gives itself.

$$16k^{2}=144$$

Divide both sides by 16.

$$k^{2}=\frac{144}{16}$$

Divide 144 by 16 to get 9.

$$k^{2}=9$$

Take the square root of both sides of the equation.

$$k=3 k=-3$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$16k^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 16\left(-144\right)}}{2\times 16}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 16\left(-144\right)}}{2\times 16}$$

Multiply -4 times 16.

$$k=\frac{0±\sqrt{-64\left(-144\right)}}{2\times 16}$$

Multiply -64 times -144.

$$k=\frac{0±\sqrt{9216}}{2\times 16}$$

Take the square root of 9216.

$$k=\frac{0±96}{2\times 16}$$

Multiply 2 times 16.

$$k=\frac{0±96}{32}$$

Now solve the equation k=\frac{0±96}{32} when ± is plus. Divide 96 by 32.

$$k=3$$

Now solve the equation k=\frac{0±96}{32} when ± is minus. Divide -96 by 32.

$$k=-3$$

The equation is now solved.

$$k=3 k=-3$$