Question 1209636: Complete the square: 3x^2 + 8x + 9 - 4x^2 + 25x + 19
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to complete the square for the given expression:
1. **Combine like terms:**
(3x² - 4x²) + (8x + 25x) + (9 + 19) = -x² + 33x + 28
2. **Factor out the coefficient of the x² term from the x² and x terms:**
-1(x² - 33x) + 28
3. **Complete the square inside the parentheses:**
Take half of the coefficient of the x term (-33), square it ((-33/2)² = 1089/4), and add and subtract it inside the parentheses:
-1(x² - 33x + 1089/4 - 1089/4) + 28
4. **Rewrite the expression:**
-1(x - 33/2)² + 1089/4 + 28
5. **Simplify the constant term:**
-1(x - 33/2)² + 1089/4 + 112/4
-1(x - 33/2)² + 1201/4
Therefore, the completed square form is: -(x - 33/2)² + 1201/4 or -(x - 16.5)² + 300.25
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