Solve 72^2-4(28)(48-3k^2)/4=0

$$\frac { 72 ^ { 2 } - 4 ( 28 ) ( 48 - 3 k ^ { 2 } ) } { 4 } = 0$$

Solve for k

$$k=\frac{2\sqrt{7}}{7}\approx 0.755928946$$

$$k=-\frac{2\sqrt{7}}{7}\approx -0.755928946$$

Steps by Finding Square Root

Multiply both sides by 4. Anything times zero gives zero.

$$72^{2}-4\times 28\left(48-3k^{2}\right)=0$$

Calculate 72 to the power of 2 and get 5184.

$$5184-4\times 28\left(48-3k^{2}\right)=0$$

Multiply 4 and 28 to get 112.

$$5184-112\left(48-3k^{2}\right)=0$$

Use the distributive property to multiply -112 by 48-3k^{2}.

$$5184-5376+336k^{2}=0$$

Subtract 5376 from 5184 to get -192.

$$-192+336k^{2}=0$$

Add 192 to both sides. Anything plus zero gives itself.

$$336k^{2}=192$$

Divide both sides by 336.

$$k^{2}=\frac{192}{336}$$

Reduce the fraction \frac{192}{336} to lowest terms by extracting and canceling out 48.

$$k^{2}=\frac{4}{7}$$

Take the square root of both sides of the equation.

$$k=\frac{2\sqrt{7}}{7} k=-\frac{2\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Multiply both sides by 4. Anything times zero gives zero.

$$72^{2}-4\times 28\left(48-3k^{2}\right)=0$$

Calculate 72 to the power of 2 and get 5184.

$$5184-4\times 28\left(48-3k^{2}\right)=0$$

Multiply 4 and 28 to get 112.

$$5184-112\left(48-3k^{2}\right)=0$$

Use the distributive property to multiply -112 by 48-3k^{2}.

$$5184-5376+336k^{2}=0$$

Subtract 5376 from 5184 to get -192.

$$-192+336k^{2}=0$$

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.

$$336k^{2}-192=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 336 for a, 0 for b, and -192 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 336\left(-192\right)}}{2\times 336}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 336\left(-192\right)}}{2\times 336}$$

Multiply -4 times 336.

$$k=\frac{0±\sqrt{-1344\left(-192\right)}}{2\times 336}$$

Multiply -1344 times -192.

$$k=\frac{0±\sqrt{258048}}{2\times 336}$$

Take the square root of 258048.

$$k=\frac{0±192\sqrt{7}}{2\times 336}$$

Multiply 2 times 336.

$$k=\frac{0±192\sqrt{7}}{672}$$

Now solve the equation k=\frac{0±192\sqrt{7}}{672} when ± is plus.

$$k=\frac{2\sqrt{7}}{7}$$

Now solve the equation k=\frac{0±192\sqrt{7}}{672} when ± is minus.

$$k=-\frac{2\sqrt{7}}{7}$$

The equation is now solved.

$$k=\frac{2\sqrt{7}}{7} k=-\frac{2\sqrt{7}}{7}$$