To rewrite the trinomial 1.5x^2 + 6x in the form a(x + b)^2 or a(x - b)^2, we need to complete the square. Here's a step-by-step guide on how to do this:
1. **Identify the coefficient of x^2:** The coefficient of x^2 is 1.5, which can be rewritten as 3/2.
2. **Factor out the coefficient of x^2:** Factor out 3/2 from 1.5x^2 + 6x to get 3/2(x^2 + 4x).
3. **Complete the square:** To complete the square, we need to add and subtract (b/2)^2 inside the parentheses. In this case, b = 4, so (4/2)^2 = 4. Add and subtract 4 inside the parentheses: 3/2(x^2 + 4x + 4 - 4).
4. **Simplify:** Rearrange the terms to create a perfect square trinomial: 3/2(x + 2)^2 - 3.
Therefore, the trinomial 1.5x^2 + 6x can be rewritten as 3/2(x + 2)^2 - 3 in the form a(x + b)^2.
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