Question

Solve the equation (1 - 0.15)*(1 0.14)(1+x)(1 0.26))¹/⁴ - 1 = 0.05.

A) x=0.10
B) x=−0.10
C) x=−0.15
D) x=0.15

Answer 1

To solve the equation (1 - 0.15)(1 + 0.14)(1+x)(1 - 0.26)^(1/4) - 1 = 0.05, you can simplify the equation and solve for x using the steps provided. The value of x that solves the equation is approximately x = 0.155.

Step-by-step explanation:

To solve the equation (1 - 0.15)(1 + 0.14)(1+x)(1 - 0.26)^(1/4) - 1 = 0.05, we can simplify the equation and solve for x. Here are the steps:

1. Expand the equation: (1 - 0.15)(1 + 0.14)(1+x)(1 - 0.26)^(1/4) - 1 = 0.05.
2. Simplify the equation: (0.85)(1.14)(1+x)(0.74)^(1/4) - 1 = 0.05.
3. Distribute and simplify further: (0.85)(1.14)(1+x)^(1/4)(0.74)^(1/4) - 1 = 0.05.
4. Combine like terms: 0.8594(1+x)^(1/4) - 1 = 0.05.
5. Add 1 to both sides: 0.8594(1+x)^(1/4) = 1.05.
6. Divide both sides by 0.8594: (1+x)^(1/4) = 1.223110.
7. Raise both sides to the power of 4: 1+x = (1.223110)^4.
8. Subtract 1 from both sides: x = (1.223110)^4 - 1.
9. Calculate the value of x: x ≈ 0.154812.

Therefore, the value of x that solves the equation is approximately x = 0.155.