# Math equation.Complete the square then solve the equation x^2 + 2x + 7 = 0.

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve x^2 + 2x + 7 = 0 by completing the square

x^2 + 2x + 7 = 0

=> x^2 + 2x + 1 = -6

=> (x + 1)^2 = -6

=> x + 1 = sqrt (-6) and x + 1 = -sqrt (-6)

=> x + 1 = i*sqrt 6 and x + 1 = -i*sqrt 6

=> x = -1 + i*sqrt 6 and x = -1 - i*sqrt 6

The solutions of x^2 + 2x + 7 = 0 are x = -1 + i*sqrt 6 and x = -1 - i*sqrt 6

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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For the beginning, we'll subtract 7 both sides, to move the constant on the right side of the equation.

x^2 + 2x = -7

We'll complete the square by adding the number 1 to both side, to obtain a square to the left side.

x^2 +2x + 1 = -7 + 1

We'll write the left side as a perfect square:

(x + 1)^2 = -6

x + 1 = sqrt -6

Since sqrt -1 = i, we'll get:

x + 1 = isqrt 6

We'll subtract 1 both sides:

x1 = -1 + isqrt 6

x2 = -1 - isqrt 6

The complex solutions of the equation are: {-1 + isqrt 6; -1 - isqrt 6}.