Answer
The length of CP is $~~1.56$
Work Step by Step
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 $~~1.56$
