What are the solutions of the equation x^2 + 4x + 5 = 0?

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Multiple Choice

What are the solutions of the equation x^2 + 4x + 5 = 0?

Explanation:
When a quadratic with real coefficients has a negative discriminant, its solutions are complex numbers. Solve by completing the square: x^2 + 4x + 5 = 0 becomes (x+2)^2 + 1 = 0. Then (x+2)^2 = -1, so x+2 = ± i and x = -2 ± i. The two roots are -2 + i and -2 - i, often written together as x = -2 ± i.

When a quadratic with real coefficients has a negative discriminant, its solutions are complex numbers. Solve by completing the square: x^2 + 4x + 5 = 0 becomes (x+2)^2 + 1 = 0. Then (x+2)^2 = -1, so x+2 = ± i and x = -2 ± i. The two roots are -2 + i and -2 - i, often written together as x = -2 ± i.

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