Question 1209268: Fill in the blanks with numbers to make a true equation.
3x^2 + 12x + 4 - 17x^2 - 18x + 22 = ___ (x + ___)^2 + ___
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! **1. Combine Like Terms**
* 3x² + 12x + 4 - 17x² - 18x + 22
* = (3x² - 17x²) + (12x - 18x) + (4 + 22)
* = -14x² - 6x + 26
**2. Complete the Square**
* **Factor out the coefficient of x²:**
-14(x² + (6/14)x) + 26
-14(x² + (3/7)x) + 26
* **Inside the parentheses, add and subtract the square of half the coefficient of x:**
-14(x² + (3/7)x + (3/14)² - (3/14)²) + 26
* **Rewrite as a perfect square trinomial:**
-14[(x + 3/14)² - 9/196] + 26
* **Distribute -14:**
-14(x + 3/14)² + 126/196 + 26
* **Simplify:**
-14(x + 3/14)² + 30.2857
**Therefore, the equation can be filled in as follows:**
3x² + 12x + 4 - 17x² - 18x + 22 = **-14** (x + **-0.2857**)² + **30.2857**
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