Solve 5d^2+11d

$$5 d ^ { 2 } + 11 d$$

Factor

$$d\left(5d+11\right)$$

Solution Steps

Factor out d.

$$d\left(5d+11\right)$$

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.

$$5d^{2}+11d=0$$

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.

$$d=\frac{-11±\sqrt{11^{2}}}{2\times 5}$$

Take the square root of 11^{2}.

$$d=\frac{-11±11}{2\times 5}$$

Multiply 2 times 5.

$$d=\frac{-11±11}{10}$$

Now solve the equation d=\frac{-11±11}{10} when ± is plus. Add -11 to 11.

$$d=\frac{0}{10}$$

Divide 0 by 10.

$$d=0$$

Now solve the equation d=\frac{-11±11}{10} when ± is minus. Subtract 11 from -11.

$$d=-\frac{22}{10}$$

Reduce the fraction \frac{-22}{10} to lowest terms by extracting and canceling out 2.

$$d=-\frac{11}{5}$$

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{11}{5} for x_{2}.

$$5d^{2}+11d=5d\left(d-\left(-\frac{11}{5}\right)\right)$$

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

$$5d^{2}+11d=5d\left(d+\frac{11}{5}\right)$$

Add \frac{11}{5} to d by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$5d^{2}+11d=5d\times \frac{5d+11}{5}$$

Cancel out 5, the greatest common factor in 5 and 5.

$$5d^{2}+11d=d\left(5d+11\right)$$

Evaluate

$$d\left(5d+11\right)$$