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Simplifying x2 + 2x + 2 = -2x2 + 8x + -7 Reorder the terms: 2 + 2x + x2 = -2x2 + 8x + -7 Reorder the terms: 2 + 2x + x2 = -7 + 8x + -2x2 Solving 2 + 2x + x2 = -7 + 8x + -2x2 Solving for variable 'x'. Reorder the terms: 2 + 7 + 2x + -8x + x2 + 2x2 = -7 + 8x + -2x2 + 7 + -8x + 2x2 Combine like terms: 2 + 7 = 9 9 + 2x + -8x + x2 + 2x2 = -7 + 8x + -2x2 + 7 + -8x + 2x2 Combine like terms: 2x + -8x = -6x 9 + -6x + x2 + 2x2 = -7 + 8x + -2x2 + 7 + -8x + 2x2 Combine like terms: x2 + 2x2 = 3x2 9 + -6x + 3x2 = -7 + 8x + -2x2 + 7 + -8x + 2x2 Reorder the terms: 9 + -6x + 3x2 = -7 + 7 + 8x + -8x + -2x2 + 2x2 Combine like terms: -7 + 7 = 0 9 + -6x + 3x2 = 0 + 8x + -8x + -2x2 + 2x2 9 + -6x + 3x2 = 8x + -8x + -2x2 + 2x2 Combine like terms: 8x + -8x = 0 9 + -6x + 3x2 = 0 + -2x2 + 2x2 9 + -6x + 3x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 9 + -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -2x + x2) = 0 Ignore the factor 3.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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