Find zeros of quadratic equation

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Homework Help Overview

The discussion revolves around finding the zeros of a quadratic equation, specifically the equation P(x)=4(x+7)^2+(x+7)-3. Participants are exploring the implications of a substitution made to simplify the problem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to substitute a variable to simplify the equation but expresses uncertainty about back substitution. Other participants question the definition of the substitution variable and suggest clarifying its relationship to the original variable.

Discussion Status

The discussion is ongoing, with participants providing guidance on the substitution process and how to revert to the original variable. There is a focus on understanding the relationship between the substituted variable and the original variable, but no consensus has been reached on the complete solution.

Contextual Notes

Participants are navigating the implications of a change of variables and the necessary steps to revert to the original equation. There is an emphasis on ensuring clarity in the substitution process and its impact on solving for the zeros of the quadratic equation.

Torshi
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Homework Statement


Find the zeros of the quadratic equation?


Homework Equations



P(x)=4(x+7)^2+(x+7)-3

The Attempt at a Solution



I substituted and made it 4u^2+u-3 ?? Then after that I factor then back substitute?? I'm not sure how to back substitute tho.
 
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Think about what u is equal to when you make the substitution. If you have that and the value for u, finding x should be straightforward.
 
Torshi said:
I'm not sure how to back substitute tho.

What's the equation for u in terms of x? Once you have this, solve for x in the equation and plug in the values you got for u.
 
You did a change of variables. You substituted u for x where u = x+7 to get the equation

f(u) \, = \, 4u^{2} \, + \, u \, - \, 3 \, = \, 0

solve for u in the above expression then use u = x + 7 to find x for each u.

i.e. since u = x+7 then x = u - 7 gives you x.
 

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