To solve the equation 53b³ + 2b² + 5 = 2b³ + 2, we first rearrange it to one side:
53b³ + 2b² + 5 – 2b³ – 2 = 0
This simplifies to:
(53b³ – 2b³) + 2b² + (5 – 2) = 0
Which further simplifies to:
51b³ + 2b² + 3 = 0
Next, we can attempt to solve for b using numerical methods or factoring, but given the complexity of the coefficients, it might not factor nicely. We can also use the Rational Root Theorem to look for possible rational solutions. Testing values can help, or we may need to employ numerical approximation methods or graphing to find the roots.
In summary, the initial equation simplifies to 51b³ + 2b² + 3 = 0, and from here we can find the value(s) of b.