Solve 2w^2+w

$$2 w ^ { 2 } + w$$

Factor

$$w\left(2w+1\right)$$

Solution Steps

Factor out w.

$$w\left(2w+1\right)$$

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.

$$2w^{2}+w=0$$

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.

$$w=\frac{-1±\sqrt{1^{2}}}{2\times 2}$$

Take the square root of 1^{2}.

$$w=\frac{-1±1}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{-1±1}{4}$$

Now solve the equation w=\frac{-1±1}{4} when ± is plus. Add -1 to 1.

$$w=\frac{0}{4}$$

Divide 0 by 4.

$$w=0$$

Now solve the equation w=\frac{-1±1}{4} when ± is minus. Subtract 1 from -1.

$$w=-\frac{2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$w=-\frac{1}{2}$$

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{1}{2} for x_{2}.

$$2w^{2}+w=2w\left(w-\left(-\frac{1}{2}\right)\right)$$

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

$$2w^{2}+w=2w\left(w+\frac{1}{2}\right)$$

Add \frac{1}{2} to w by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$2w^{2}+w=2w\times \frac{2w+1}{2}$$

Cancel out 2, the greatest common factor in 2 and 2.

$$2w^{2}+w=w\left(2w+1\right)$$

Evaluate

$$w\left(2w+1\right)$$