# Help Solve Lost Soul's S=an^2+bn Equation Problem

• Erectable
In summary, the problem is to find the values of constants a and b in the equation S = an^2 + bn, given the possible values of S and n. The suggested approach is to solve for a and b using a system of equations, but the individual has had trouble finding a solution using this method and is considering using the quadratic formula instead. However, it is suggested that the problem may have been overcomplicated and that choosing two equations and solving for a and b may lead to a solution. The remaining equations can then be used to test the validity of the solution.
Erectable
The problem is:

S = an^2 + bn

Where a and b are constants.

Possible values for S are: 6, 15, 27, 42 and 60
Possible values for n are: 1 when S=6, 2 when S=15, 3 when S=27, 4 when S=42 and 5, when S=60.

I am asked to find the values of a and b.

The way I tried to tackle it was sort it out into quadratic form:

an^2 + bn - s = 0

I then substituted suitable values for n and s. After that, I rearrange the equation so I can get the value of of either b or a and try to solve it using simultaneous equations.

I've tried many times to find the values of a or b but everytime I end up with a 0 = 0 scenario and in the case of S=60 and n=5:

0(5^2) + 0(5) - 60 does not equal 0.

My other idea is to use quadratic formula somehow to find the coefficients of n^2 and n but I can't find anything about solving it this way.

I would appreciate it if somebody with a good sturdy brain could please help a dumb richard like myself.

I'm afraid if I tell you, you're going to murder yourself. You've definitely overcomplicated the entire problem.

Given that information we can sub in values for S and n respectively to develop the following equations:

\begin{align*} 6 &= a(1)^{2} + b(1)\\ &= a + b\\ \\ 15 &= a(2)^{2} + b(2)\\ &= 4a + 2b\\ \\ 27 &= a(3)^{2} + b(3)\\ &= 9a + 3b\\ \\ 42 &= a(4)^{2} + b(4)\\ &= 16a + 4b\\ \\ 60 &= a(5)^{2} + b(5)\\ &= 25a + 5b\\ \end{align*}

We don't even need all of those equations. Three fifths of those equations are redundant. We can take any two (it's easiest to take the first two) and solve for a and b with the classic "system of equations". Elimination, to be precise. I hope this is all you need. You should be able to take it from here.

Last edited:
This problem ask you to use two equations to solve two unknowns, or else there's an infinite number of solutions for a and b.

Ok, as others have pointed out. So just choose 2 equations randomly, the 2 that you think you like best from the 5 equations above. Then solve for a, and b.
Then we use the 3 rest equations to test, i.e, we'll plug the value of a, and b in the 3 equations. If they all hold, then a, and b are your solutions. If one of them does not hold, then this system of equations has no solution. Can you get this?
Canyou go from here? :)

## 1. What is the "Help Solve Lost Soul's S=an^2+bn Equation Problem"?

The "Help Solve Lost Soul's S=an^2+bn Equation Problem" is a mathematical problem that involves finding the values of variables "a" and "b" in the equation S=an^2+bn, where "n" is a given number. The goal is to solve for "a" and "b" in order to find the value of "S".

## 2. Why is this problem important?

This problem is important because it helps develop critical thinking and problem-solving skills. It also allows for the application of mathematical concepts such as algebra and equations in real-world situations.

## 3. What are the possible solutions for this problem?

The possible solutions for this problem are infinite, as there are infinite values for "a" and "b" that can satisfy the equation. However, in most cases, there is a unique solution that can be found using algebraic methods.

## 4. How can I approach this problem?

The best way to approach this problem is to first simplify the equation by factoring out the common factor, if possible. Then, you can use algebraic methods such as substitution or elimination to solve for the unknown variables.

## 5. Can this problem be solved using a calculator or software?

Yes, this problem can be solved using a calculator or software that has the capability to solve equations. However, it is important to have a good understanding of algebraic concepts and methods in order to verify the accuracy of the solution.

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