Answer:
B. 02(x+6)2 = 20
Explanation:
The minimum value for the equation 2x2 + 12x - 14 = 0 can be found by completing the square.
To complete the square for a quadratic equation in the form ax2 + bx + c, we first need to divide both sides of the equation by the coefficient of x2, which is 2 in this case. This gives us:
x2 + 6x - 7 = 0
Now to complete the square, we calculate half the coefficient of x, which is 6/2 = 3. We then square this value and add it to both sides:
x2 + 6x - 7 + 9= 9
(x + 3)2 = 2
Factoring the left side gives us:
2(x + 3)2 = 20
We can now set (x + 3)2 equal to 0 to find the minimum/maximum values:
(x + 3)2 = 0
x + 3 = 0
x = -3
Therefore, the value of x that minimizes 2x2 + 12x - 14 is -3.
Of the given options, only Option B reveals this minimum value