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Simplifying x2 + -2x + 1 = -1x2 + -4x + -7 Reorder the terms: 1 + -2x + x2 = -1x2 + -4x + -7 Reorder the terms: 1 + -2x + x2 = -7 + -4x + -1x2 Solving 1 + -2x + x2 = -7 + -4x + -1x2 Solving for variable 'x'. Reorder the terms: 1 + 7 + -2x + 4x + x2 + x2 = -7 + -4x + -1x2 + 7 + 4x + x2 Combine like terms: 1 + 7 = 8 8 + -2x + 4x + x2 + x2 = -7 + -4x + -1x2 + 7 + 4x + x2 Combine like terms: -2x + 4x = 2x 8 + 2x + x2 + x2 = -7 + -4x + -1x2 + 7 + 4x + x2 Combine like terms: x2 + x2 = 2x2 8 + 2x + 2x2 = -7 + -4x + -1x2 + 7 + 4x + x2 Reorder the terms: 8 + 2x + 2x2 = -7 + 7 + -4x + 4x + -1x2 + x2 Combine like terms: -7 + 7 = 0 8 + 2x + 2x2 = 0 + -4x + 4x + -1x2 + x2 8 + 2x + 2x2 = -4x + 4x + -1x2 + x2 Combine like terms: -4x + 4x = 0 8 + 2x + 2x2 = 0 + -1x2 + x2 8 + 2x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 8 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + x + x2)' equal to zero and attempt to solve: Simplifying 4 + x + x2 = 0 Solving 4 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x + x2 = 0 + -4 x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x + x2 = -4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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