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Simplifying x + -5 = 2x(2x + 1) Reorder the terms: -5 + x = 2x(2x + 1) Reorder the terms: -5 + x = 2x(1 + 2x) -5 + x = (1 * 2x + 2x * 2x) -5 + x = (2x + 4x2) Solving -5 + x = 2x + 4x2 Solving for variable 'x'. Combine like terms: x + -2x = -1x -5 + -1x + -4x2 = 2x + 4x2 + -2x + -4x2 Reorder the terms: -5 + -1x + -4x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 -5 + -1x + -4x2 = 0 + 4x2 + -4x2 -5 + -1x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + -1x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + x + 4x2 = 0 Solving 5 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.25x + x2 = 0 + -1.25 0.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.25x + x2 = -1.25 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. 0.25x + 0.25 + x2 = -1.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 0.25 + 0.25x + x2 = -1 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1 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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