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