Solve (13/4div3)+1/4=cquadc=

$$( 1 \frac { 3 } { 4 } \div 3 ) + \frac { 1 } { 4 } = c \quad c =$$

Solve for c

$$c=\frac{\sqrt{30}}{6}\approx 0.912870929$$

$$c=-\frac{\sqrt{30}}{6}\approx -0.912870929$$

Steps by Finding Square Root

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4\times \frac{1\times 4+3}{4}+3=12cc$$

Multiply c and c to get c^{2}.

$$4\times \frac{1\times 4+3}{4}+3=12c^{2}$$

Multiply 1 and 4 to get 4.

$$4\times \frac{4+3}{4}+3=12c^{2}$$

Add 4 and 3 to get 7.

$$4\times \frac{7}{4}+3=12c^{2}$$

Cancel out 4 and 4.

$$7+3=12c^{2}$$

Add 7 and 3 to get 10.

$$10=12c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$12c^{2}=10$$

Divide both sides by 12.

$$c^{2}=\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$c^{2}=\frac{5}{6}$$

Take the square root of both sides of the equation.

$$c=\frac{\sqrt{30}}{6} c=-\frac{\sqrt{30}}{6}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4\times \frac{1\times 4+3}{4}+3=12cc$$

Multiply c and c to get c^{2}.

$$4\times \frac{1\times 4+3}{4}+3=12c^{2}$$

Multiply 1 and 4 to get 4.

$$4\times \frac{4+3}{4}+3=12c^{2}$$

Add 4 and 3 to get 7.

$$4\times \frac{7}{4}+3=12c^{2}$$

Cancel out 4 and 4.

$$7+3=12c^{2}$$

Add 7 and 3 to get 10.

$$10=12c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$12c^{2}=10$$

Subtract 10 from both sides.

$$12c^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\times 12\left(-10\right)}}{2\times 12}$$

Square 0.

$$c=\frac{0±\sqrt{-4\times 12\left(-10\right)}}{2\times 12}$$

Multiply -4 times 12.

$$c=\frac{0±\sqrt{-48\left(-10\right)}}{2\times 12}$$

Multiply -48 times -10.

$$c=\frac{0±\sqrt{480}}{2\times 12}$$

Take the square root of 480.

$$c=\frac{0±4\sqrt{30}}{2\times 12}$$

Multiply 2 times 12.

$$c=\frac{0±4\sqrt{30}}{24}$$

Now solve the equation c=\frac{0±4\sqrt{30}}{24} when ± is plus.

$$c=\frac{\sqrt{30}}{6}$$

Now solve the equation c=\frac{0±4\sqrt{30}}{24} when ± is minus.

$$c=-\frac{\sqrt{30}}{6}$$

The equation is now solved.

$$c=\frac{\sqrt{30}}{6} c=-\frac{\sqrt{30}}{6}$$