Solve xi^2+3xi

$$\xi ^ { 2 } + 3 \xi$$

Factor

$$\xi \left(\xi +3\right)$$

Solution Steps

Factor out \xi .

$$\xi \left(\xi +3\right)$$

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.

$$\xi ^{2}+3\xi =0$$

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.

$$\xi =\frac{-3±\sqrt{3^{2}}}{2}$$

Take the square root of 3^{2}.

$$\xi =\frac{-3±3}{2}$$

Now solve the equation \xi =\frac{-3±3}{2} when ± is plus. Add -3 to 3.

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

Divide 0 by 2.

$$\xi =0$$

Now solve the equation \xi =\frac{-3±3}{2} when ± is minus. Subtract 3 from -3.

$$\xi =-\frac{6}{2}$$

Divide -6 by 2.

$$\xi =-3$$

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 -3 for x_{2}.

$$\xi ^{2}+3\xi =\xi \left(\xi -\left(-3\right)\right)$$

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

$$\xi ^{2}+3\xi =\xi \left(\xi +3\right)$$

Evaluate

$$\xi \left(\xi +3\right)$$