Solve V(x)=20x^2+200x

$$V ( x ) = 20 x ^ { 2 } + 200 x$$

Factor

$$20x\left(x+10\right)$$

Solution Steps

Factor out 20.

$$20\left(x^{2}+10x\right)$$

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

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

Rewrite the complete factored expression.

$$20x\left(x+10\right)$$

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.

$$20x^{2}+200x=0$$

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.

$$x=\frac{-200±\sqrt{200^{2}}}{2\times 20}$$

Take the square root of 200^{2}.

$$x=\frac{-200±200}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{-200±200}{40}$$

Now solve the equation x=\frac{-200±200}{40} when ± is plus. Add -200 to 200.

$$x=\frac{0}{40}$$

Divide 0 by 40.

$$x=0$$

Now solve the equation x=\frac{-200±200}{40} when ± is minus. Subtract 200 from -200.

$$x=-\frac{400}{40}$$

Divide -400 by 40.

$$x=-10$$

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 -10 for x_{2}.

$$20x^{2}+200x=20x\left(x-\left(-10\right)\right)$$

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

$$20x^{2}+200x=20x\left(x+10\right)$$

Evaluate

$$20x\left(x+10\right)$$