Answer:
p ≈ 0.842 and p ≈ -1.842
Explanation:
To solve the equation 5(p - 1)p = 8, we can begin by expanding the expression:
5(p - 1)p = 8
5(p^2 - p) = 8
Distribute the 5:
5p^2 - 5p = 8
Rearrange the equation to bring all terms to one side:
5p^2 - 5p - 8 = 0
Now we have a quadratic equation. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:
Given an equation in the form ax^2 + bx + c = 0, the quadratic formula states that the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 5, b = -5, and c = -8. Substituting these values into the quadratic formula, we get:
p = (-(-5) ± √((-5)^2 - 4(5)(-8))) / (2(5))
p = (5 ± √(25 + 160)) / 10
p = (5 ± √185) / 10
The solutions for p are given by p ≈ 0.842 and p ≈ -1.842.