What is the solution to the following equation x²+3x+7=0

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Data

Equation     x² + 3x + 7 = 0

Let's solve this equation by two methods.

1) Completing the perfect square trinomial

                 x² + 3x      = -7

                 x² + 3x + (3/2)² = -7 + (3/2)²

                (x + 3/2)² = -7 + 9/4

                 (x + 3/2)² = -19/4

                 x + 3/2 = √-19/√4

                 x = -3/2 + √-19/2         It has imaginary solutions.

2.- Graph the equation

See the graph below.

In the graph we notice that the equation does not cross the x-axis so it does not have real solution.

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step-by-step explanation:

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