Solve 103-c^2/112=13/14

$$\frac { 103 - c ^ { 2 } } { 112 } = \frac { 13 } { 14 }$$

Solve for c

$$c=i$$

$$c=-i$$

Steps by Finding Square Root

Multiply both sides by 112.

$$103-c^{2}=\frac{13}{14}\times 112$$

Multiply \frac{13}{14} and 112 to get 104.

$$103-c^{2}=104$$

Subtract 103 from both sides.

$$-c^{2}=104-103$$

Subtract 103 from 104 to get 1.

$$-c^{2}=1$$

Divide both sides by -1.

$$c^{2}=-1$$

The equation is now solved.

$$c=i c=-i$$

Steps Using the Quadratic Formula

Multiply both sides by 112.

$$103-c^{2}=\frac{13}{14}\times 112$$

Multiply \frac{13}{14} and 112 to get 104.

$$103-c^{2}=104$$

Subtract 104 from both sides.

$$103-c^{2}-104=0$$

Subtract 104 from 103 to get -1.

$$-1-c^{2}=0$$

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.

$$-c^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$c=\frac{0±\sqrt{4\left(-1\right)}}{2\left(-1\right)}$$

Multiply 4 times -1.

$$c=\frac{0±\sqrt{-4}}{2\left(-1\right)}$$

Take the square root of -4.

$$c=\frac{0±2i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$c=\frac{0±2i}{-2}$$

Now solve the equation c=\frac{0±2i}{-2} when ± is plus.

$$c=-i$$

Now solve the equation c=\frac{0±2i}{-2} when ± is minus.

$$c=i$$

The equation is now solved.

$$c=-i c=i$$