Solve 49+56-c^2/2*56=13/14

$$\frac{ 49+56- { c }^{ 2 } }{ 2 \times 56 } = \frac{ 13 }{ 14 }$$

Solve for c

$$c=1$$

$$c=-1$$

Steps by Finding Square Root

Add 49 and 56 to get 105.

$$\frac{105-c^{2}}{2\times 56}=\frac{13}{14}$$

Multiply 2 and 56 to get 112.

$$\frac{105-c^{2}}{112}=\frac{13}{14}$$

Divide each term of 105-c^{2} by 112 to get \frac{15}{16}-\frac{1}{112}c^{2}.

$$\frac{15}{16}-\frac{1}{112}c^{2}=\frac{13}{14}$$

Subtract \frac{15}{16} from both sides.

$$-\frac{1}{112}c^{2}=\frac{13}{14}-\frac{15}{16}$$

Subtract \frac{15}{16} from \frac{13}{14} to get -\frac{1}{112}.

$$-\frac{1}{112}c^{2}=-\frac{1}{112}$$

Multiply both sides by -112, the reciprocal of -\frac{1}{112}.

$$c^{2}=-\frac{1}{112}\left(-112\right)$$

Multiply -\frac{1}{112} and -112 to get 1.

$$c^{2}=1$$

Take the square root of both sides of the equation.

$$c=1 c=-1$$

Steps Using the Quadratic Formula

Add 49 and 56 to get 105.

$$\frac{105-c^{2}}{2\times 56}=\frac{13}{14}$$

Multiply 2 and 56 to get 112.

$$\frac{105-c^{2}}{112}=\frac{13}{14}$$

Divide each term of 105-c^{2} by 112 to get \frac{15}{16}-\frac{1}{112}c^{2}.

$$\frac{15}{16}-\frac{1}{112}c^{2}=\frac{13}{14}$$

Subtract \frac{13}{14} from both sides.

$$\frac{15}{16}-\frac{1}{112}c^{2}-\frac{13}{14}=0$$

Subtract \frac{13}{14} from \frac{15}{16} to get \frac{1}{112}.

$$\frac{1}{112}-\frac{1}{112}c^{2}=0$$

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.

$$-\frac{1}{112}c^{2}+\frac{1}{112}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{112} for a, 0 for b, and \frac{1}{112} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{112}\right)\times \frac{1}{112}}}{2\left(-\frac{1}{112}\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-\frac{1}{112}\right)\times \frac{1}{112}}}{2\left(-\frac{1}{112}\right)}$$

Multiply -4 times -\frac{1}{112}.

$$c=\frac{0±\sqrt{\frac{1}{28}\times \frac{1}{112}}}{2\left(-\frac{1}{112}\right)}$$

Multiply \frac{1}{28} times \frac{1}{112} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$c=\frac{0±\sqrt{\frac{1}{3136}}}{2\left(-\frac{1}{112}\right)}$$

Take the square root of \frac{1}{3136}.

$$c=\frac{0±\frac{1}{56}}{2\left(-\frac{1}{112}\right)}$$

Multiply 2 times -\frac{1}{112}.

$$c=\frac{0±\frac{1}{56}}{-\frac{1}{56}}$$

Now solve the equation c=\frac{0±\frac{1}{56}}{-\frac{1}{56}} when ± is plus.

$$c=-1$$

Now solve the equation c=\frac{0±\frac{1}{56}}{-\frac{1}{56}} when ± is minus.

$$c=1$$

The equation is now solved.

$$c=-1 c=1$$