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Simplifying -2x(2x + 1) = x + 5 Reorder the terms: -2x(1 + 2x) = x + 5 (1 * -2x + 2x * -2x) = x + 5 (-2x + -4x2) = x + 5 Reorder the terms: -2x + -4x2 = 5 + x Solving -2x + -4x2 = 5 + x Solving for variable 'x'. Reorder the terms: -5 + -2x + -1x + -4x2 = 5 + x + -5 + -1x Combine like terms: -2x + -1x = -3x -5 + -3x + -4x2 = 5 + x + -5 + -1x Reorder the terms: -5 + -3x + -4x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 -5 + -3x + -4x2 = 0 + x + -1x -5 + -3x + -4x2 = x + -1x Combine like terms: x + -1x = 0 -5 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75x + x2 = 0 + -1.25 0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75x + x2 = -1.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.109375 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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