Solve 26x^2+200x

$$26 x ^ { 2 } + 200 x$$

Factor

$$2x\left(13x+100\right)$$

Solution Steps

Factor out 2.

$$2\left(13x^{2}+100x\right)$$

Consider 13x^{2}+100x. Factor out x.

$$x\left(13x+100\right)$$

Rewrite the complete factored expression.

$$2x\left(13x+100\right)$$

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.

$$26x^{2}+200x=0$$

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.

$$x=\frac{-200±\sqrt{200^{2}}}{2\times 26}$$

Take the square root of 200^{2}.

$$x=\frac{-200±200}{2\times 26}$$

Multiply 2 times 26.

$$x=\frac{-200±200}{52}$$

Now solve the equation x=\frac{-200±200}{52} when ± is plus. Add -200 to 200.

$$x=\frac{0}{52}$$

Divide 0 by 52.

$$x=0$$

Now solve the equation x=\frac{-200±200}{52} when ± is minus. Subtract 200 from -200.

$$x=-\frac{400}{52}$$

Reduce the fraction \frac{-400}{52} to lowest terms by extracting and canceling out 4.

$$x=-\frac{100}{13}$$

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 -\frac{100}{13} for x_{2}.

$$26x^{2}+200x=26x\left(x-\left(-\frac{100}{13}\right)\right)$$

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

$$26x^{2}+200x=26x\left(x+\frac{100}{13}\right)$$

Add \frac{100}{13} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$26x^{2}+200x=26x\times \frac{13x+100}{13}$$

Cancel out 13, the greatest common factor in 26 and 13.

$$26x^{2}+200x=2x\left(13x+100\right)$$

Evaluate

$$2x\left(13x+100\right)$$