Solve 5x^2-25x

$$5 x ^ { 2 } - 25 x$$

Factor

$$5x\left(x-5\right)$$

Solution Steps

Factor out 5.

$$5\left(x^{2}-5x\right)$$

Consider x^{2}-5x. Factor out x.

$$x\left(x-5\right)$$

Rewrite the complete factored expression.

$$5x\left(x-5\right)$$

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.

$$5x^{2}-25x=0$$

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.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}}}{2\times 5}$$

Take the square root of \left(-25\right)^{2}.

$$x=\frac{-\left(-25\right)±25}{2\times 5}$$

The opposite of -25 is 25.

$$x=\frac{25±25}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{25±25}{10}$$

Now solve the equation x=\frac{25±25}{10} when ± is plus. Add 25 to 25.

$$x=\frac{50}{10}$$

Divide 50 by 10.

$$x=5$$

Now solve the equation x=\frac{25±25}{10} when ± is minus. Subtract 25 from 25.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 5 for x_{1} and 0 for x_{2}.

$$5x^{2}-25x=5\left(x-5\right)x$$

Evaluate

$$5x\left(x-5\right)$$