- #1
dbn
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if you can solve ax^2-40x+40=0 for a and x that would be great
Can You Solve ax^2-40x+40=0 for Both a and x?
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SUMMARY
The equation ax2 - 40x + 40 = 0 presents a scenario with two unknowns, a and x, and one equation, making it impossible to find unique solutions for both variables. By applying the quadratic formula, x can be expressed in terms of a as x = (20 ± 2√(10(10 - a)))/a. Alternatively, a can be expressed in terms of x using the rearranged formula a = 40(x - 1)/x2. This establishes that for any non-zero x, there is a corresponding single value for a.
PREREQUISITES- Understanding of quadratic equations and their properties
- Familiarity with the quadratic formula
- Basic algebraic manipulation skills
- Knowledge of expressing variables in terms of one another
- Study the derivation and applications of the quadratic formula
- Explore the concept of expressing one variable in terms of another in algebra
- Learn about the implications of having multiple unknowns in equations
- Investigate the graphical representation of quadratic equations and their solutions
Students, educators, and anyone interested in algebraic problem-solving, particularly those dealing with quadratic equations and variable relationships.
- #2
AKG
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No. We have two unknowns (a and x) and one equation. At best, we can express a in terms of x, and vice versa, but no better. To express x in terms of a, simply apply the quadratic formula to the equation you have. You'll get:
x = \frac{20 \pm 2\sqrt{10(10 - a)}}{a}
x = \frac{20 \pm 2\sqrt{10(10 - a)}}{a}
- #3
PRodQuanta
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use this formula \frac{-b ^+_- \sqrt{b^2 - 4ac}}{2a}where a=a, b=-40 and c=40
Paden Roder
- #4
PRodQuanta
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Well, sorry! I just stated the quadratic formula, as AKG said. This was the first time I have used LaTeX though, pretty cool, once you get the hang of it.
Paden Roder
Paden Roder
- #5
dbn
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i still don't get it can some one give me a walk through on how to use them with this problem/
- #6
dbn
- 3
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a= 0 x= 1
i just fount it
i just fount it
- #7
phreak
- 133
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*groan*
I bet there are millions of answers for this one.
I came up with a = 10, x = 2
I bet there are millions of answers for this one.
I came up with a = 10, x = 2
- #8
Zorodius
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phreak said:
I bet there's more than that. In fact, I bet the set of all possible answers is uncountably infinite. I'd bet a lot of money on it, since, as AKG said, with one equation and two unknowns, this isn't going to go anywhere.
- #9
arildno
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Now, while the others have shown how to find x given a, here's how you may find the a-value for any choice of x-value:dbn said:
ax^{2}-40x+40=0
Rewrite this as:
a=40\frac{x-1}{x^{2}}
Hence, for any non-zero choice of x, only a single value for a is allowed by the equation.
- #10
KnowledgeIsPower
- 89
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Is this the whole question?
Unless it's an 'express x in terms of a' type question you can't solve it with only that information.
Unless it's an 'express x in terms of a' type question you can't solve it with only that information.