Solve x^2 + (-1/2x + 5)^2 = 25

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Homework Help Overview

The discussion revolves around solving the equation x^2 + (-1/2x + 5)^2 = 25, which falls under the subject area of algebra, specifically quadratic equations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss expanding the squared term and simplifying the equation. There is a clarification regarding the interpretation of the expression, questioning whether it is meant as ((-1/2)x + 5)^2 or (-1/(2x) + 5)^2.

Discussion Status

The discussion is active, with participants providing guidance on expanding the equation and addressing potential ambiguities in the expression. There is an ongoing exploration of different interpretations of the original equation.

Contextual Notes

Participants are navigating assumptions about the structure of the equation, particularly regarding the placement of parentheses and the implications for solving the quadratic.

Spruance
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How do we solve this equation:


x^2 + (-1/2x + 5)^2 = 25

Thanks in advance
 
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Expand that squared term and you'll see that this quadratic equation simplifies nicely.
 
That's assuming that you mean ((-1/2)x + 5)^2 and not (-1/(2x)+ 5)^2.
 
Thanks, then

x^2 + (-x/2 + 5)^2 = 25

x2 + x2/4 - 5x + 25 = 25

5x2/4 - 5x = 0 (* 4/5)

x2 - 4x = 0

x(x - 4) = 0

x = 0 or x = 4.
 

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