Solve (18)^2-4(9)(16k^2-135)=0

$$( 18 ) ^ { 2 } - 4 ( 9 ) ( 16 k ^ { 2 } - 135 ) = 0$$

Solve for k

$$k=3$$

$$k=-3$$

Steps by Finding Square Root

Calculate 18 to the power of 2 and get 324.

$$324-4\times 9\left(16k^{2}-135\right)=0$$

Multiply 4 and 9 to get 36.

$$324-36\left(16k^{2}-135\right)=0$$

Use the distributive property to multiply -36 by 16k^{2}-135.

$$324-576k^{2}+4860=0$$

Add 324 and 4860 to get 5184.

$$5184-576k^{2}=0$$

Subtract 5184 from both sides. Anything subtracted from zero gives its negation.

$$-576k^{2}=-5184$$

Divide both sides by -576.

$$k^{2}=\frac{-5184}{-576}$$

Divide -5184 by -576 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

Calculate 18 to the power of 2 and get 324.

$$324-4\times 9\left(16k^{2}-135\right)=0$$

Multiply 4 and 9 to get 36.

$$324-36\left(16k^{2}-135\right)=0$$

Use the distributive property to multiply -36 by 16k^{2}-135.

$$324-576k^{2}+4860=0$$

Add 324 and 4860 to get 5184.

$$5184-576k^{2}=0$$

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.

$$-576k^{2}+5184=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -576 for a, 0 for b, and 5184 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-576\right)\times 5184}}{2\left(-576\right)}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-576\right)\times 5184}}{2\left(-576\right)}$$

Multiply -4 times -576.

$$k=\frac{0±\sqrt{2304\times 5184}}{2\left(-576\right)}$$

Multiply 2304 times 5184.

$$k=\frac{0±\sqrt{11943936}}{2\left(-576\right)}$$

Take the square root of 11943936.

$$k=\frac{0±3456}{2\left(-576\right)}$$

Multiply 2 times -576.

$$k=\frac{0±3456}{-1152}$$

Now solve the equation k=\frac{0±3456}{-1152} when ± is plus. Divide 3456 by -1152.

$$k=-3$$

Now solve the equation k=\frac{0±3456}{-1152} when ± is minus. Divide -3456 by -1152.

$$k=3$$

The equation is now solved.

$$k=-3 k=3$$