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Simplifying x2 + -2x + -31 = -7 + 4x2 + 2x Reorder the terms: -31 + -2x + x2 = -7 + 4x2 + 2x Reorder the terms: -31 + -2x + x2 = -7 + 2x + 4x2 Solving -31 + -2x + x2 = -7 + 2x + 4x2 Solving for variable 'x'. Reorder the terms: -31 + 7 + -2x + -2x + x2 + -4x2 = -7 + 2x + 4x2 + 7 + -2x + -4x2 Combine like terms: -31 + 7 = -24 -24 + -2x + -2x + x2 + -4x2 = -7 + 2x + 4x2 + 7 + -2x + -4x2 Combine like terms: -2x + -2x = -4x -24 + -4x + x2 + -4x2 = -7 + 2x + 4x2 + 7 + -2x + -4x2 Combine like terms: x2 + -4x2 = -3x2 -24 + -4x + -3x2 = -7 + 2x + 4x2 + 7 + -2x + -4x2 Reorder the terms: -24 + -4x + -3x2 = -7 + 7 + 2x + -2x + 4x2 + -4x2 Combine like terms: -7 + 7 = 0 -24 + -4x + -3x2 = 0 + 2x + -2x + 4x2 + -4x2 -24 + -4x + -3x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 -24 + -4x + -3x2 = 0 + 4x2 + -4x2 -24 + -4x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24 + -4x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 4x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 24 + 4x + 3x2 = 0 Solving 24 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 1.333333333x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 1.333333333x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 1.333333333x + x2 = 0 + -8 1.333333333x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 1.333333333x + x2 = -8 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -8 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -8 + 0.4444444442 Combine like terms: -8 + 0.4444444442 = -7.5555555558 0.4444444442 + 1.333333333x + x2 = -7.5555555558 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -7.5555555558 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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