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[(1.08)(1+x)] 1/2- 1 =10 what is x?

Guest Jun 4, 2017
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 #1
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I read your equation thus: [(1.08)(1+x)]^1/2- 1 =10, solve for x

Solve for x:
1.03923 sqrt(x + 1) - 1 = 10

Add 1 to both sides:
1.03923 sqrt(x + 1) = 11

Divide both sides by 1.03923:
sqrt(x + 1) = 10.5848

Raise both sides to the power of two:
x + 1 = 112.037

Subtract 1 from both sides:
Answer: | x = 111.037

Guest Jun 4, 2017
 #4
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Thank you for your assistance!

Guest Jun 6, 2017
 #2
avatar+1493 
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I am only showing this alternate solution because I think it is a nicer way of solving it than what the guest provided. His/her method, though, is sound and is perfectly fine. 

 

 

\([(1.08)(1+x)]^{\frac{1}{2}}-1=10\) Add 1 on both sides
\([(1.08)(1+x)]^{\frac{1}{2}}=11\) Simplify \((1.08)(1+x)\) by distributing the 1.08 to the 1 and the x.
\((1.08+1.08x)^{\frac{1}{2}}=11\) Taking something to the power of 1/2 is the same as square root, so let's write it like that
\(\sqrt{1.08+1.08x}=11\) Square both sides to get rid of the radical
\(1.08+1.08x=121\) Subtract 1.08 on both sides 
\(1.08x=119.92\) Divide by 1.08 on both sides to isolate x.
\(x=\frac{119.92}{1.08}\) Multiply the numerator and denominator by 100 to make them whole numbers
\(x=\frac{11992}{108}\div\frac{4}{4}\) Divide the numerator and denominator by its GCF, 4, to put the improper fraction in simplest terms.
\(x=\frac{2998}{27}=111.\overline{037037}\) You are done! This is your final answer!
   
TheXSquaredFactor  Jun 4, 2017
edited by TheXSquaredFactor  Jun 5, 2017
 #5
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Thank you for helping!

Guest Jun 6, 2017
 #3
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[(1.08)(1+x)] 1/2-1=10

[(.54)(.5+x)]-1=10

(-.54)(-.5+x)=10

-.54-.5+x=10

1.04+x=10

-1.04      -1.04

x=8.96

 

I looked at the other answers and I'm a freshman going into sophomore year taking geometry so, don't look at this as laugh.

Guest Jun 5, 2017

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