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What values of b satisfy 3(2b + 3)² = 36?

User SteveP
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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

(2b + 3)² = 12

2. Take the square root of both sides:

√[(2b + 3)²] = √12

Simplifying further:

2b + 3 = ±√12

3. Subtract 3 from both sides:

2b = ±√12 - 3

4. Divide both sides by 2:

b = (±√12 - 3) / 2

Simplifying further:

b = (±√4 * √3 - 3) / 2

b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

User Wendie
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