Solve 7k^2+9k

$$7 { k }^{ 2 } +9k$$

Factor

$$k\left(7k+9\right)$$

Solution Steps

Factor out k.

$$k\left(7k+9\right)$$

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.

$$7k^{2}+9k=0$$

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.

$$k=\frac{-9±\sqrt{9^{2}}}{2\times 7}$$

Take the square root of 9^{2}.

$$k=\frac{-9±9}{2\times 7}$$

Multiply 2 times 7.

$$k=\frac{-9±9}{14}$$

Now solve the equation k=\frac{-9±9}{14} when ± is plus. Add -9 to 9.

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

Divide 0 by 14.

$$k=0$$

Now solve the equation k=\frac{-9±9}{14} when ± is minus. Subtract 9 from -9.

$$k=-\frac{18}{14}$$

Reduce the fraction \frac{-18}{14} to lowest terms by extracting and canceling out 2.

$$k=-\frac{9}{7}$$

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{9}{7} for x_{2}.

$$7k^{2}+9k=7k\left(k-\left(-\frac{9}{7}\right)\right)$$

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

$$7k^{2}+9k=7k\left(k+\frac{9}{7}\right)$$

Add \frac{9}{7} to k by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$7k^{2}+9k=7k\times \frac{7k+9}{7}$$

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

$$7k^{2}+9k=k\left(7k+9\right)$$

Evaluate

$$k\left(7k+9\right)$$