Solve 14b-9b^2

$$14 b - 9 b ^ { 2 }$$

Factor

$$b\left(14-9b\right)$$

Solution Steps

Factor out b.

$$b\left(14-9b\right)$$

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.

$$-9b^{2}+14b=0$$

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.

$$b=\frac{-14±\sqrt{14^{2}}}{2\left(-9\right)}$$

Take the square root of 14^{2}.

$$b=\frac{-14±14}{2\left(-9\right)}$$

Multiply 2 times -9.

$$b=\frac{-14±14}{-18}$$

Now solve the equation b=\frac{-14±14}{-18} when ± is plus. Add -14 to 14.

$$b=\frac{0}{-18}$$

Divide 0 by -18.

$$b=0$$

Now solve the equation b=\frac{-14±14}{-18} when ± is minus. Subtract 14 from -14.

$$b=-\frac{28}{-18}$$

Reduce the fraction \frac{-28}{-18} to lowest terms by extracting and canceling out 2.

$$b=\frac{14}{9}$$

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{14}{9} for x_{2}.

$$-9b^{2}+14b=-9b\left(b-\frac{14}{9}\right)$$

Subtract \frac{14}{9} from b by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-9b^{2}+14b=-9b\times \frac{-9b+14}{-9}$$

Cancel out 9, the greatest common factor in -9 and -9.

$$-9b^{2}+14b=b\left(-9b+14\right)$$

Evaluate

$$b\left(14-9b\right)$$