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Simplifying x + 3 = x2 + 3x + 6 Reorder the terms: 3 + x = x2 + 3x + 6 Reorder the terms: 3 + x = 6 + 3x + x2 Solving 3 + x = 6 + 3x + x2 Solving for variable 'x'. Reorder the terms: 3 + -6 + x + -3x + -1x2 = 6 + 3x + x2 + -6 + -3x + -1x2 Combine like terms: 3 + -6 = -3 -3 + x + -3x + -1x2 = 6 + 3x + x2 + -6 + -3x + -1x2 Combine like terms: x + -3x = -2x -3 + -2x + -1x2 = 6 + 3x + x2 + -6 + -3x + -1x2 Reorder the terms: -3 + -2x + -1x2 = 6 + -6 + 3x + -3x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -3 + -2x + -1x2 = 0 + 3x + -3x + x2 + -1x2 -3 + -2x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -3 + -2x + -1x2 = 0 + x2 + -1x2 -3 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 2x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2x + x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + x2 = 0 Solving 3 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + x2 = 0 + -3 2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x + x2 = -3 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -3 + 1 Reorder the terms: 1 + 2x + x2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2x + x2 = -2 Factor a perfect square on the left side: (x + 1)(x + 1) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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