Rearranging Equations to Find x in Terms of a and b | Homework Help

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Homework Help Overview

The discussion revolves around rearranging the equation a(a+x)=b(b-x) to express x in terms of a and b, with the condition that a≠-b. Participants are exploring algebraic manipulation techniques to isolate x.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss multiplying out the brackets and moving terms to isolate x. There are attempts to clarify the process of rearranging equations and the implications of moving terms across the equality.

Discussion Status

The discussion includes various approaches to rearranging the equation, with some participants offering guidance on how to group terms. There is an ongoing exploration of the steps involved, and while one participant proposes a potential solution, another questions the correctness of the steps taken.

Contextual Notes

Participants are working under the assumption that a and b are variables with specific conditions, and there is a focus on ensuring the manipulation adheres to algebraic rules. The original poster expresses uncertainty about the next steps after their initial attempt.

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Homework Statement



I need to rearrange the following equation to find x in terms of a and b, assuming that a≠-b

Homework Equations



a(a+x)=b(b-x)


The Attempt at a Solution



So far I have multiplied out the brackets and came up with

a^{}2+ax=b^{}2-bx

but I don't really know where to go from there to find x in terms of a and b.Would be really grateful if someone could help. Thanks.
 
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Try adding and subtracting terms from each side so you get each x term on the same side.
 
you can move things over from the left to the right or vice versa i.e.

a + b = d - e
can become by moving things around:

a + b - d = -e

notice how we change the sign when things move over!

for ur question u want to get the x's on one side as the next step so move things over to get the x's together and the a's and b's together.
 
So would this be right?:

ax-bx=a2-b2
x(a-b)=a2-b2
x=(a2-b2)/(a-b)
 
Note ax+bx=b2-a2 and you have to correct your steps
 

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