Question 1209634: Complete the square: x^2 - 10x + 21 + 3x^2 - 2x + 8.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 1. **Combine like terms:**
* (x² + 3x²) + (-10x - 2x) + (21 + 8)
* 4x² - 12x + 29
2. **Factor out the coefficient of the x² term from the x² and x terms:**
* 4(x² - 3x) + 29
3. **Complete the square inside the parentheses:**
* Take half of the coefficient of the x term (-3), which is -3/2.
* Square it: (-3/2)² = 9/4
Add and subtract this value *inside* the parentheses:
* 4(x² - 3x + 9/4 - 9/4) + 29
4. **Rewrite as a squared term:**
* 4(x - 3/2)² - 4(9/4) + 29
5. **Simplify:**
* 4(x - 3/2)² - 9 + 29
* 4(x - 3/2)² + 20
Therefore, the completed square form is 4(x - 3/2)² + 20.
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