Solve -5x^2-50x

$$-5 { x }^{ 2 } -50x$$

Factor

$$-5x\left(x+10\right)$$

Solution Steps

Factor out 5.

$$5\left(-x^{2}-10x\right)$$

Consider -x^{2}-10x. Factor out x.

$$x\left(-x-10\right)$$

Rewrite the complete factored expression.

$$5x\left(-x-10\right)$$

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.

$$-5x^{2}-50x=0$$

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.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}}}{2\left(-5\right)}$$

Take the square root of \left(-50\right)^{2}.

$$x=\frac{-\left(-50\right)±50}{2\left(-5\right)}$$

The opposite of -50 is 50.

$$x=\frac{50±50}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{50±50}{-10}$$

Now solve the equation x=\frac{50±50}{-10} when ± is plus. Add 50 to 50.

$$x=\frac{100}{-10}$$

Divide 100 by -10.

$$x=-10$$

Now solve the equation x=\frac{50±50}{-10} when ± is minus. Subtract 50 from 50.

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

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 -10 for x_{1} and 0 for x_{2}.

$$-5x^{2}-50x=-5\left(x-\left(-10\right)\right)x$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$-5x^{2}-50x=-5\left(x+10\right)x$$

Evaluate

$$-5x\left(x+10\right)$$