Solve 17x^2+51x

$$17 x ^ { 2 } + 51 x$$

Factor

$$17x\left(x+3\right)$$

Solution Steps

Factor out 17.

$$17\left(x^{2}+3x\right)$$

Consider x^{2}+3x. Factor out x.

$$x\left(x+3\right)$$

Rewrite the complete factored expression.

$$17x\left(x+3\right)$$

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.

$$17x^{2}+51x=0$$

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.

$$x=\frac{-51±\sqrt{51^{2}}}{2\times 17}$$

Take the square root of 51^{2}.

$$x=\frac{-51±51}{2\times 17}$$

Multiply 2 times 17.

$$x=\frac{-51±51}{34}$$

Now solve the equation x=\frac{-51±51}{34} when ± is plus. Add -51 to 51.

$$x=\frac{0}{34}$$

Divide 0 by 34.

$$x=0$$

Now solve the equation x=\frac{-51±51}{34} when ± is minus. Subtract 51 from -51.

$$x=-\frac{102}{34}$$

Divide -102 by 34.

$$x=-3$$

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 -3 for x_{2}.

$$17x^{2}+51x=17x\left(x-\left(-3\right)\right)$$

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

$$17x^{2}+51x=17x\left(x+3\right)$$

Evaluate

$$17x\left(x+3\right)$$