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
+2441 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! |
