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Simplifying -2x(x + 2) = -2x + 1 Reorder the terms: -2x(2 + x) = -2x + 1 (2 * -2x + x * -2x) = -2x + 1 (-4x + -2x2) = -2x + 1 Reorder the terms: -4x + -2x2 = 1 + -2x Solving -4x + -2x2 = 1 + -2x Solving for variable 'x'. Reorder the terms: -1 + -4x + 2x + -2x2 = 1 + -2x + -1 + 2x Combine like terms: -4x + 2x = -2x -1 + -2x + -2x2 = 1 + -2x + -1 + 2x Reorder the terms: -1 + -2x + -2x2 = 1 + -1 + -2x + 2x Combine like terms: 1 + -1 = 0 -1 + -2x + -2x2 = 0 + -2x + 2x -1 + -2x + -2x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -1 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 2x2 = 0 Solving 1 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x + x2 = 0 + -0.5 x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x + x2 = -0.5 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. + 0.25 + x2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 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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