Final answer:
To complete the square in the equation x² + 4x = 12, rearrange the equation, add and subtract a value, and simplify to obtain the equivalent equation (x + 2)² = 28.
Step-by-step explanation:
To complete the square in the equation x² + 4x = 12, we need to rearrange the equation by moving the constant term to the other side of the equation. This gives us x² + 4x - 12 = 0. Next, we take half of the coefficient of x, which is 4, and square it to get 4² = 16. We add this value to both sides of the equation: x² + 4x + 16 - 12 = 16. Simplifying, we have (x + 2)² = 28, which is the equivalent equation after completing the square.
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