Final answer:
To solve the quadratic equation -4r² = -8r + 2, we can use the quadratic formula: r = (-b ± √(b² - 4ac)) / (2a). Substituting the values, we get: r = -1 + √6 / 2 and r = -1 - √6 / 2.
Step-by-step explanation:
This expression is a quadratic equation of the form -4r² = -8r + 2, where a = -4, b = -8, and c = 2. To solve for r, we can use the quadratic formula:
r = (-b ± √(b² - 4ac)) / (2a)
Substituting the values, we get:
r = (-(-8) ± √((-8)² - 4(-4)(2))) / (2(-4))
r = (8 ± √(64 + 32)) / (-8)
r = (8 ± √96) / (-8)
r = (8 ± 4√6) / (-8)
r = -1 ± √6 / 2
Therefore, the solutions to the equation are r = -1 + √6 / 2 and r = -1 - √6 / 2.