Solve 13x^2+26x

$$13 { x }^{ 2 } +26x$$

Factor

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

Solution Steps

Factor out 13.

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

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

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

Rewrite the complete factored expression.

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

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.

$$13x^{2}+26x=0$$

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.

$$x=\frac{-26±\sqrt{26^{2}}}{2\times 13}$$

Take the square root of 26^{2}.

$$x=\frac{-26±26}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{-26±26}{26}$$

Now solve the equation x=\frac{-26±26}{26} when ± is plus. Add -26 to 26.

$$x=\frac{0}{26}$$

Divide 0 by 26.

$$x=0$$

Now solve the equation x=\frac{-26±26}{26} when ± is minus. Subtract 26 from -26.

$$x=-\frac{52}{26}$$

Divide -52 by 26.

$$x=-2$$

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 -2 for x_{2}.

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

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

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

Evaluate

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