Question
Solve using the quadratic formula
8=3n^2+10n
8=3n^2+10n
Answers
GPT 3.5
To solve the equation 8 = 3n^2 + 10n using the quadratic formula, we can rewrite it in the form ax^2 + bx + c = 0 by subtracting 8 from both sides:
3n^2 + 10n - 8 = 0
Now we can identify a = 3, b = 10, and c = -8. Plugging these values into the quadratic formula, which states that x = (-b ± √(b^2 - 4ac)) / (2a), we get:
n = (-10 ± √(10^2 - 4(3)(-8))) / (2(3))
Simplifying further:
n = (-10 ± √(100 + 96)) / 6
n = (-10 ± √196) / 6
n = (-10 ± 14) / 6
This gives us two possible solutions:
n = (4 / 6) or n = (-24 / 6)
Simplifying:
n = 2/3 or n = -4
So the solutions to the equation 8 = 3n^2 + 10n are n = 2/3 and n = -4.
3n^2 + 10n - 8 = 0
Now we can identify a = 3, b = 10, and c = -8. Plugging these values into the quadratic formula, which states that x = (-b ± √(b^2 - 4ac)) / (2a), we get:
n = (-10 ± √(10^2 - 4(3)(-8))) / (2(3))
Simplifying further:
n = (-10 ± √(100 + 96)) / 6
n = (-10 ± √196) / 6
n = (-10 ± 14) / 6
This gives us two possible solutions:
n = (4 / 6) or n = (-24 / 6)
Simplifying:
n = 2/3 or n = -4
So the solutions to the equation 8 = 3n^2 + 10n are n = 2/3 and n = -4.