Solving for a variable. Hard to do in this simple equation.

In summary, the problem at hand is to solve for "a" in the equation a(a+b+c)=d. The solution involves using the distributive property to get a^2+ab+ac=d, and then dividing both sides by "a" to get a+b+c=d. From there, subtracting "a" and "d" yields b+c-d=-a. However, it is important to note that you cannot divide only one side of an equation, so the solution also involves using the Quadratic Formula to solve for "a".
  • #1
Jon9992
4
0
Hi. This isn't for any sort of homework. I've run into a deadend where I have a situation like this where I need to solve for "a":

a(a+b+c) =d

You'd think it would be easy but I can't seem to get "a" by itself. It always end up on both sides of the equation at best which is starting to make me think it's somehow recursive. I know how to solve it if it didn't have the "c" by using the quadratic equation but not sure in this situation.

Thanks so much!
 
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  • #2
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d. Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.
 
  • #3
Gbl911 said:
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d.
Absolutely not! You can't divide just one side of an equation. If you divide the left side by a, you have to also divide the right side by a.
Gb said:
Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.

After carrying out the multiplication on the left side, you get a2 + ab + ac = d. Add -d to both sides to get a2 + ab + ac - d = 0. One more step gets us to a2 + (b + c)a - d = 0. This is a quadratic in a, and can be solved for a by using the Quadratic Formula.
 

1. How do I solve for a variable in a simple equation?

In order to solve for a variable in a simple equation, you need to isolate the variable on one side of the equation by using inverse operations. This means performing the opposite operation of what is being done to the variable. For example, if the variable is being multiplied by a number, you would divide both sides by that number to isolate the variable.

2. What is the first step in solving for a variable?

The first step in solving for a variable is to simplify the equation by combining like terms and applying the order of operations. This will help make the equation easier to work with and understand.

3. Can I solve for a variable if there are multiple variables in the equation?

Yes, you can still solve for a specific variable even if there are multiple variables in the equation. Just treat the other variables as constants and follow the same steps for solving for a variable.

4. What should I do if there are fractions involved in the equation?

If there are fractions involved in the equation, you can eliminate them by multiplying both sides of the equation by the least common denominator (LCD) of all the fractions. This will help simplify the equation and make it easier to solve for the variable.

5. How do I know if I have solved for the variable correctly?

You can check your answer by plugging in the solved variable into the original equation and seeing if it makes the equation true. If it does, then you have solved for the variable correctly. It is always important to double-check your work to avoid any mistakes.

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