Solve 11c^2+7c

$$11 c ^ { 2 } + 7 c$$

Factor

$$c\left(11c+7\right)$$

Solution Steps

Factor out c.

$$c\left(11c+7\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$11c^{2}+7c=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$c=\frac{-7±\sqrt{7^{2}}}{2\times 11}$$

Take the square root of 7^{2}.

$$c=\frac{-7±7}{2\times 11}$$

Multiply 2 times 11.

$$c=\frac{-7±7}{22}$$

Now solve the equation c=\frac{-7±7}{22} when ± is plus. Add -7 to 7.

$$c=\frac{0}{22}$$

Divide 0 by 22.

$$c=0$$

Now solve the equation c=\frac{-7±7}{22} when ± is minus. Subtract 7 from -7.

$$c=-\frac{14}{22}$$

Reduce the fraction \frac{-14}{22} to lowest terms by extracting and canceling out 2.

$$c=-\frac{7}{11}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{7}{11} for x_{2}.

$$11c^{2}+7c=11c\left(c-\left(-\frac{7}{11}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$11c^{2}+7c=11c\left(c+\frac{7}{11}\right)$$

Add \frac{7}{11} to c by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$11c^{2}+7c=11c\times \frac{11c+7}{11}$$

Cancel out 11, the greatest common factor in 11 and 11.

$$11c^{2}+7c=c\left(11c+7\right)$$

Evaluate

$$c\left(11c+7\right)$$