Solve 16c^2-10^2(c^2-9)=0

$$16 c ^ { 2 } - 10 ^ { 2 } ( c ^ { 2 } - 9 ) = 0$$

Solve for c

$$c = \frac{5 \sqrt{21}}{7} \approx 3.273268354$$

$$c = -\frac{5 \sqrt{21}}{7} \approx -3.273268354$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$16c^{2}-100\left(c^{2}-9\right)=0$$

Use the distributive property to multiply -100 by c^{2}-9.

$$16c^{2}-100c^{2}+900=0$$

Combine 16c^{2} and -100c^{2} to get -84c^{2}.

$$-84c^{2}+900=0$$

Subtract 900 from both sides. Anything subtracted from zero gives its negation.

$$-84c^{2}=-900$$

Divide both sides by -84.

$$c^{2}=\frac{-900}{-84}$$

Reduce the fraction \frac{-900}{-84} to lowest terms by extracting and canceling out -12.

$$c^{2}=\frac{75}{7}$$

Take the square root of both sides of the equation.

$$c=\frac{5\sqrt{21}}{7} c=-\frac{5\sqrt{21}}{7}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$16c^{2}-100\left(c^{2}-9\right)=0$$

Use the distributive property to multiply -100 by c^{2}-9.

$$16c^{2}-100c^{2}+900=0$$

Combine 16c^{2} and -100c^{2} to get -84c^{2}.

$$-84c^{2}+900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -84 for a, 0 for b, and 900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-84\right)\times 900}}{2\left(-84\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-84\right)\times 900}}{2\left(-84\right)}$$

Multiply -4 times -84.

$$c=\frac{0±\sqrt{336\times 900}}{2\left(-84\right)}$$

Multiply 336 times 900.

$$c=\frac{0±\sqrt{302400}}{2\left(-84\right)}$$

Take the square root of 302400.

$$c=\frac{0±120\sqrt{21}}{2\left(-84\right)}$$

Multiply 2 times -84.

$$c=\frac{0±120\sqrt{21}}{-168}$$

Now solve the equation c=\frac{0±120\sqrt{21}}{-168} when ± is plus.

$$c=-\frac{5\sqrt{21}}{7}$$

Now solve the equation c=\frac{0±120\sqrt{21}}{-168} when ± is minus.

$$c=\frac{5\sqrt{21}}{7}$$

The equation is now solved.

$$c=-\frac{5\sqrt{21}}{7} c=\frac{5\sqrt{21}}{7}$$