Question

Please solve this equation, as I'm stuck: c² + 2cd - 15d².

a) (c + 3d)(c - 5d)
b) (c - 3d)(c + 5d)
c) (c - 3d)(c - 5d)
d) (c + 3d)(c + 5d)

Answer 1

The quadratic equation can be solved using the quadratic formula, yielding x = 10 or x = -20.

Step-by-step explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1.00, b = 10.0, and c = -200. Its solutions are given by the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the appropriate values for a, b, and c yields:

x = (-10.0 ± √((10.0)² - 4(1.00)(-200))) / (2(1.00))

Simplifying the equation further:

x = (-10.0 ± √(100 + 800)) / 2

x = (-10.0 ± √900) / 2

x = (-10.0 ± 30) / 2

x = (-10.0 + 30) / 2 or x = (-10.0 - 30) / 2

x = 20 / 2 or x = -40 / 2

x = 10 or x = -20