Answer: 6(x - (23/2))² = 14x + 1044
Explanation:
First, we need to move all the terms to one side of the equation:
6x² - 46x - 312 - 14x = 0
Next, we need to factor out the coefficient of the x² term:
6(x² - (46/6)x) - 312 - 14x = 0
Simplifying:
6(x² - 23x) - 312 - 14x = 0
To complete the square, we need to add and subtract the square of half the coefficient of the x-term inside the parentheses:
6[(x - (23/2))² - (23/2)²] - 312 - 14x = 0
Simplifying:
6(x - (23/2))² - 6(23/2)² - 312 - 14x = 0
Expanding the square term:
6(x - (23/2))² - 1044 - 14x = 0
Finally, adding 1044 to both sides and simplifying:
6(x - (23/2))² = 14x + 1044
The intermediate step after completing the square is:
6(x - (23/2))² = 14x + 1044