Solve 49w^2-24w

$$49 w ^ { 2 } - 24 w$$

Factor

$$w\left(49w-24\right)$$

Solution Steps

Factor out w.

$$w\left(49w-24\right)$$

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.

$$49w^{2}-24w=0$$

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.

$$w=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 49}$$

Take the square root of \left(-24\right)^{2}.

$$w=\frac{-\left(-24\right)±24}{2\times 49}$$

The opposite of -24 is 24.

$$w=\frac{24±24}{2\times 49}$$

Multiply 2 times 49.

$$w=\frac{24±24}{98}$$

Now solve the equation w=\frac{24±24}{98} when ± is plus. Add 24 to 24.

$$w=\frac{48}{98}$$

Reduce the fraction \frac{48}{98} to lowest terms by extracting and canceling out 2.

$$w=\frac{24}{49}$$

Now solve the equation w=\frac{24±24}{98} when ± is minus. Subtract 24 from 24.

$$w=\frac{0}{98}$$

Divide 0 by 98.

$$w=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{24}{49} for x_{1} and 0 for x_{2}.

$$49w^{2}-24w=49\left(w-\frac{24}{49}\right)w$$

Subtract \frac{24}{49} from w by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$49w^{2}-24w=49\times \frac{49w-24}{49}w$$

Cancel out 49, the greatest common factor in 49 and 49.

$$49w^{2}-24w=\left(49w-24\right)w$$

Evaluate

$$w\left(49w-24\right)$$