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Simplifying x2 + 6x + 3 = 0 Reorder the terms: 3 + 6x + x2 = 0 Solving 3 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6x + x2 = 0 + -3 6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 6x + x2 = -3 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -3 + 9 Reorder the terms: 9 + 6x + x2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + 6x + x2 = 6 Factor a perfect square on the left side: (x + 3)(x + 3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 3) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 3 = 2.449489743 Simplifying x + 3 = 2.449489743 Reorder the terms: 3 + x = 2.449489743 Solving 3 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.449489743 + -3 x = 2.449489743 + -3 Combine like terms: 2.449489743 + -3 = -0.550510257 x = -0.550510257 Simplifying x = -0.550510257Subproblem 2
x + 3 = -2.449489743 Simplifying x + 3 = -2.449489743 Reorder the terms: 3 + x = -2.449489743 Solving 3 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.449489743 + -3 x = -2.449489743 + -3 Combine like terms: -2.449489743 + -3 = -5.449489743 x = -5.449489743 Simplifying x = -5.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.550510257, -5.449489743}
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