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Destinyyyy
 one year ago
Solve the equation by making an appropriate substitution.
Destinyyyy
 one year ago
Solve the equation by making an appropriate substitution.

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1let u=x^(1) then u^2=x^(2)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and you should be factoring u^2+3u10 right now

freckles
 one year ago
Best ResponseYou've already chosen the best response.1neat so you can solve the equation (u2)(u+5)=0 for u

freckles
 one year ago
Best ResponseYou've already chosen the best response.1now remember we replace x^(1) with u so we have to undo that replacement by replacing u with x^(1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[x^{1}=2 \text{ or } 5 \\ x^{1}=2 \text{ or } x^{1}=5 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1recall x^(1) is the same thing as saying 1/x

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{x}=2 \text{ or } \frac{1}{x}=5 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1can you solve both of those equations for x

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0?? x^2=2 you have two 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{x}=a \\ \text{ multiply both sides by } x \\ 1=ax \\ \text{ divide both sides by } a \\ \frac{1}{a}=x \\ \text{ so assuming } x \neq 0 \text{ and } a \neq 0 \\ \text{ then } \frac{1}{x}=a \implies x=\frac{1}{a}\]

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0Um okay I think I understand that but dont see how that solves this.. :/

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0Dont I just square root both sides?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you have 1/x=2 so x=1/2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you have 1/x=5 so x=?

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0So thats the answer?

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0Do I check it? Or no?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1another way to solve this is multiply both sides of your equation by x^2 \[x^{2}+3x^{1}10=0 \\ x^2(x^{2}+3x^{1}10)=x^{2}(0) \\ x^{2+(2)}+3x^{2+(1)}10x^{2}=0 \\ x^{0}+3x^{1}10x^2=0 \\ 10x^2+3x+1=0 \text{ since } x^{0}=1 \text{ and I just reorder terms } \\ 10x^2+5x2x+1=0 \\ 5x(2x1)1(2x1)=0 \\ (2x1)(5x1)=0 \\ 2x1=0 \text{ when } x=\frac{1}{2} \\ 5x1=0 \text{ when } x=\frac{1}{5}\] there is no harm in checking but the answers are fine we didn't raise both sides to an even power and are answers fit in with domain of the original equation (for this question we definitely did not want x=0 as a solution which we didn't have to worry about here)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oh I see what you did about you replace u with x^(2) even though u equals x^(1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1anyways if you have more questions post a new question I'm gonna take a short break

freckles
 one year ago
Best ResponseYou've already chosen the best response.1unless you have questions on this one then I can stay and answer them real quick

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok I will be back later! peace for now! :)

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.0Sorry didnt see you send back.
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