Solve -2x^2-10x

$$-2 { x }^{ 2 } -10x$$

Factor

$$-2x\left(x+5\right)$$

Solution Steps

Factor out 2.

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

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

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

Rewrite the complete factored expression.

$$2x\left(-x-5\right)$$

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.

$$-2x^{2}-10x=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\left(-2\right)}$$

Take the square root of \left(-10\right)^{2}.

$$x=\frac{-\left(-10\right)±10}{2\left(-2\right)}$$

The opposite of -10 is 10.

$$x=\frac{10±10}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{10±10}{-4}$$

Now solve the equation x=\frac{10±10}{-4} when ± is plus. Add 10 to 10.

$$x=\frac{20}{-4}$$

Divide 20 by -4.

$$x=-5$$

Now solve the equation x=\frac{10±10}{-4} when ± is minus. Subtract 10 from 10.

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

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}.

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

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

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

Evaluate

$$-2x\left(x+5\right)$$