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Simplifying x2 + 2x + 2 = 2x2 + 4x + 7 Reorder the terms: 2 + 2x + x2 = 2x2 + 4x + 7 Reorder the terms: 2 + 2x + x2 = 7 + 4x + 2x2 Solving 2 + 2x + x2 = 7 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: 2 + -7 + 2x + -4x + x2 + -2x2 = 7 + 4x + 2x2 + -7 + -4x + -2x2 Combine like terms: 2 + -7 = -5 -5 + 2x + -4x + x2 + -2x2 = 7 + 4x + 2x2 + -7 + -4x + -2x2 Combine like terms: 2x + -4x = -2x -5 + -2x + x2 + -2x2 = 7 + 4x + 2x2 + -7 + -4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -5 + -2x + -1x2 = 7 + 4x + 2x2 + -7 + -4x + -2x2 Reorder the terms: -5 + -2x + -1x2 = 7 + -7 + 4x + -4x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -5 + -2x + -1x2 = 0 + 4x + -4x + 2x2 + -2x2 -5 + -2x + -1x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -5 + -2x + -1x2 = 0 + 2x2 + -2x2 -5 + -2x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 2x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x + x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + x2 = 0 Solving 5 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x + x2 = 0 + -5 2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 2x + x2 = -5 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 = -5 + 1 Reorder the terms: 1 + 2x + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + 2x + x2 = -4 Factor a perfect square on the left side: (x + 1)(x + 1) = -4 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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