Solve 17y^2+85y

$$17 y ^ { 2 } + 85 y$$

Factor

$$17y\left(y+5\right)$$

Solution Steps

Factor out 17.

$$17\left(y^{2}+5y\right)$$

Consider y^{2}+5y. Factor out y.

$$y\left(y+5\right)$$

Rewrite the complete factored expression.

$$17y\left(y+5\right)$$

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.

$$17y^{2}+85y=0$$

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.

$$y=\frac{-85±\sqrt{85^{2}}}{2\times 17}$$

Take the square root of 85^{2}.

$$y=\frac{-85±85}{2\times 17}$$

Multiply 2 times 17.

$$y=\frac{-85±85}{34}$$

Now solve the equation y=\frac{-85±85}{34} when ± is plus. Add -85 to 85.

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

Divide 0 by 34.

$$y=0$$

Now solve the equation y=\frac{-85±85}{34} when ± is minus. Subtract 85 from -85.

$$y=-\frac{170}{34}$$

Divide -170 by 34.

$$y=-5$$

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 -5 for x_{2}.

$$17y^{2}+85y=17y\left(y-\left(-5\right)\right)$$

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

$$17y^{2}+85y=17y\left(y+5\right)$$

Evaluate

$$17y\left(y+5\right)$$