Solve -9k^2-9k

$$- 9 k ^ { 2 } - 9 k$$

Factor

$$-9k\left(k+1\right)$$

Solution Steps

Factor out 9.

$$9\left(-k^{2}-k\right)$$

Consider -k^{2}-k. Factor out k.

$$k\left(-k-1\right)$$

Rewrite the complete factored expression.

$$9k\left(-k-1\right)$$

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.

$$-9k^{2}-9k=0$$

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.

$$k=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\left(-9\right)}$$

Take the square root of \left(-9\right)^{2}.

$$k=\frac{-\left(-9\right)±9}{2\left(-9\right)}$$

The opposite of -9 is 9.

$$k=\frac{9±9}{2\left(-9\right)}$$

Multiply 2 times -9.

$$k=\frac{9±9}{-18}$$

Now solve the equation k=\frac{9±9}{-18} when ± is plus. Add 9 to 9.

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

Divide 18 by -18.

$$k=-1$$

Now solve the equation k=\frac{9±9}{-18} when ± is minus. Subtract 9 from 9.

$$k=\frac{0}{-18}$$

Divide 0 by -18.

$$k=0$$

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

$$-9k^{2}-9k=-9\left(k-\left(-1\right)\right)k$$

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

$$-9k^{2}-9k=-9\left(k+1\right)k$$

Evaluate

$$-9k\left(k+1\right)$$