## Elementary Geometry for College Students (6th Edition)

The length of CP is $~~1.56$
We can rearrange the given equation as a quadratic equation: $x~(x+5) = (x+1)~4$ $x^2+5x = 4x+4$ $x^2+x-4 = 0$ We can use the quadratic formula to find the solutions of the equation: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ $x = \frac{-(1) \pm \sqrt{(1)^2-(4)(1)(-4)}}{(2)(1)}$ $x = \frac{-1 \pm \sqrt{1+16}}{2}$ $x = \frac{-1 \pm \sqrt{17}}{2}$ $x = \frac{-1 - \sqrt{17}}{2}~~$ or $~~x = \frac{-1 + \sqrt{17}}{2}$ $x = -2.56~~$ or $~~x = 1.56$ Since the length $x$ must be positive, the length of CP is $~~1.56$