Solve Q^2+6Q

$$Q ^ { 2 } + 6 Q$$

Factor

$$Q\left(Q+6\right)$$

Solution Steps

Factor out Q.

$$Q\left(Q+6\right)$$

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.

$$Q^{2}+6Q=0$$

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.

$$Q=\frac{-6±\sqrt{6^{2}}}{2}$$

Take the square root of 6^{2}.

$$Q=\frac{-6±6}{2}$$

Now solve the equation Q=\frac{-6±6}{2} when ± is plus. Add -6 to 6.

$$Q=\frac{0}{2}$$

Divide 0 by 2.

$$Q=0$$

Now solve the equation Q=\frac{-6±6}{2} when ± is minus. Subtract 6 from -6.

$$Q=-\frac{12}{2}$$

Divide -12 by 2.

$$Q=-6$$

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 -6 for x_{2}.

$$Q^{2}+6Q=Q\left(Q-\left(-6\right)\right)$$

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

$$Q^{2}+6Q=Q\left(Q+6\right)$$

Evaluate

$$Q\left(Q+6\right)$$