Solve 2w^2-42w

$$2 w ^ { 2 } - 42 w$$

Factor

$$2w\left(w-21\right)$$

Solution Steps

Factor out 2.

$$2\left(w^{2}-21w\right)$$

Consider w^{2}-21w. Factor out w.

$$w\left(w-21\right)$$

Rewrite the complete factored expression.

$$2w\left(w-21\right)$$

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.

$$2w^{2}-42w=0$$

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.

$$w=\frac{-\left(-42\right)±\sqrt{\left(-42\right)^{2}}}{2\times 2}$$

Take the square root of \left(-42\right)^{2}.

$$w=\frac{-\left(-42\right)±42}{2\times 2}$$

The opposite of -42 is 42.

$$w=\frac{42±42}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{42±42}{4}$$

Now solve the equation w=\frac{42±42}{4} when ± is plus. Add 42 to 42.

$$w=\frac{84}{4}$$

Divide 84 by 4.

$$w=21$$

Now solve the equation w=\frac{42±42}{4} when ± is minus. Subtract 42 from 42.

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

Divide 0 by 4.

$$w=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 21 for x_{1} and 0 for x_{2}.

$$2w^{2}-42w=2\left(w-21\right)w$$

Evaluate

$$2w\left(w-21\right)$$