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Simplifying 2x + 1 = 6x + 2x2 + 5 Reorder the terms: 1 + 2x = 6x + 2x2 + 5 Reorder the terms: 1 + 2x = 5 + 6x + 2x2 Solving 1 + 2x = 5 + 6x + 2x2 Solving for variable 'x'. Reorder the terms: 1 + -5 + 2x + -6x + -2x2 = 5 + 6x + 2x2 + -5 + -6x + -2x2 Combine like terms: 1 + -5 = -4 -4 + 2x + -6x + -2x2 = 5 + 6x + 2x2 + -5 + -6x + -2x2 Combine like terms: 2x + -6x = -4x -4 + -4x + -2x2 = 5 + 6x + 2x2 + -5 + -6x + -2x2 Reorder the terms: -4 + -4x + -2x2 = 5 + -5 + 6x + -6x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -4 + -4x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 -4 + -4x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -4 + -4x + -2x2 = 0 + 2x2 + -2x2 -4 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 2x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 2x + x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + x2 = 0 Solving 2 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2x + x2 = 0 + -2 2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2x + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + 2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2x + x2 = -1 Factor a perfect square on the left side: (x + 1)(x + 1) = -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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