To find the values of b that satisfy the equation 43b² + 2 = 64, we first need to isolate the b² term. We can do this by following these steps:
- Subtract 2 from both sides:
- Next, divide both sides by 43:
- Now, we take the square root of both sides:
- b = √(62/43)
- b = -√(62/43)
This gives us:
43b² = 64 - 2
Which simplifies to:
43b² = 62
b² = 62 / 43
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b = ±√(62 / 43)
This results in two potential solutions for b:
To provide numerical approximations:
- Calculating √(62 / 43) gives us approximately 1.041.
- Thus, the two values of b can be rounded to approximately 1.041 and -1.041.
In conclusion, the values of b that satisfy the equation 43b² + 2 = 64 are approximately:
- b ≈ 1.041
- b ≈ -1.041