Can you please help to solve this problem:
3n2^ + 10n = 5
Thank you
Do you mean?
3n2^
or
3n^2
3n2^...n to the second power
this is solving for a quadratic equation using the quadratic formula, but I am not sure how to solve.
n to the second power is n^2
If it's quadratic formula, then I think it would be 3n^2 + 10n - 5 = 0, then you'd have to factor that.
To solve the equation 3n^2 + 10n = 5, we need to find the value(s) of n that satisfy this equation.
Step 1: Start by subtracting 5 from both sides of the equation to isolate the quadratic term:
3n^2 + 10n - 5 = 0
Step 2: This is now a quadratic equation in standard form (ax^2 + bx + c = 0), with a = 3, b = 10, and c = -5.
Step 3: To solve this quadratic equation, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, plugging in the values from our equation, we have:
n = (-10 ± √(10^2 - 4(3)(-5))) / 2(3)
Step 4: Simplifying the expression under the square root:
n = (-10 ± √(100 + 60)) / 6
n = (-10 ± √160) / 6
n = (-10 ± 4√10) / 6
Step 5: Simplify further if possible:
n = (-5 ± 2√10) / 3
So, the solutions to the equation 3n^2 + 10n = 5 are n = (-5 + 2√10) / 3 and n = (-5 - 2√10) / 3.