Question

complete the square to solve the following quadratic equation: x^2 + 4c - 6 = 2. Is the following correct: x= -2 + 2 ^3, -2 - 2 ^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To complete the square and solve the quadratic equation x^2 + 4c - 6 = 2, we follow these steps:

1. Move the constant term to the right side of the equation:
x^2 + 4c = 8

2. Group the x terms together and leave a space on the right side for completing the square:
(x^2 + 4c + ___) = 8

3. Identify the coefficient of x, divide it by 2, and square it. Add this value inside the parentheses on the left side. Don't forget to subtract it outside of the parentheses on the right side:
(x^2 + 4c + (4/2)^2) = 8 + (4/2)^2
(x^2 + 4c + 2^2) = 8 + 2^2
(x^2 + 4c + 4) = 8 + 4
(x^2 + 4c + 4) = 12

4. Express the left side as a perfect square:
(x + 2)^2 = 12

5. Take the square root of both sides and consider both positive and negative values for the right side:
x + 2 = ±√12

6. Simplify the square root of 12:
x + 2 = ±2√3

7. Solve for x:
x = -2 ± 2√3

Therefore, the correct solution to the quadratic equation x^2 + 4c - 6 = 2, after completing the square, is:
x = -2 ± 2√3