Solve 15x^2-47x

$$15 x ^ { 2 } - 47 x$$

Factor

$$x\left(15x-47\right)$$

Solution Steps

Factor out x.

$$x\left(15x-47\right)$$

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.

$$15x^{2}-47x=0$$

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.

$$x=\frac{-\left(-47\right)±\sqrt{\left(-47\right)^{2}}}{2\times 15}$$

Take the square root of \left(-47\right)^{2}.

$$x=\frac{-\left(-47\right)±47}{2\times 15}$$

The opposite of -47 is 47.

$$x=\frac{47±47}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{47±47}{30}$$

Now solve the equation x=\frac{47±47}{30} when ± is plus. Add 47 to 47.

$$x=\frac{94}{30}$$

Reduce the fraction \frac{94}{30} to lowest terms by extracting and canceling out 2.

$$x=\frac{47}{15}$$

Now solve the equation x=\frac{47±47}{30} when ± is minus. Subtract 47 from 47.

$$x=\frac{0}{30}$$

Divide 0 by 30.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{47}{15} for x_{1} and 0 for x_{2}.

$$15x^{2}-47x=15\left(x-\frac{47}{15}\right)x$$

Subtract \frac{47}{15} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$15x^{2}-47x=15\times \frac{15x-47}{15}x$$

Cancel out 15, the greatest common factor in 15 and 15.

$$15x^{2}-47x=\left(15x-47\right)x$$

Evaluate

$$x\left(15x-47\right)$$