Solve 7t^2+11t

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

Factor

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

Solution Steps

Factor out t.

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

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.

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

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.

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

Take the square root of 11^{2}.

$$t=\frac{-11±11}{2\times 7}$$

Multiply 2 times 7.

$$t=\frac{-11±11}{14}$$

Now solve the equation t=\frac{-11±11}{14} when ± is plus. Add -11 to 11.

$$t=\frac{0}{14}$$

Divide 0 by 14.

$$t=0$$

Now solve the equation t=\frac{-11±11}{14} when ± is minus. Subtract 11 from -11.

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

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

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

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}{7} for x_{2}.

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

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

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

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

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

Cancel out 7, the greatest common factor in 7 and 7.

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

Evaluate

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