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Simplifying 3x2 + -4x + 6x = -1x2 + 6x + -2 Reorder the terms: -4x + 6x + 3x2 = -1x2 + 6x + -2 Combine like terms: -4x + 6x = 2x 2x + 3x2 = -1x2 + 6x + -2 Reorder the terms: 2x + 3x2 = -2 + 6x + -1x2 Solving 2x + 3x2 = -2 + 6x + -1x2 Solving for variable 'x'. Reorder the terms: 2 + 2x + -6x + 3x2 + x2 = -2 + 6x + -1x2 + 2 + -6x + x2 Combine like terms: 2x + -6x = -4x 2 + -4x + 3x2 + x2 = -2 + 6x + -1x2 + 2 + -6x + x2 Combine like terms: 3x2 + x2 = 4x2 2 + -4x + 4x2 = -2 + 6x + -1x2 + 2 + -6x + x2 Reorder the terms: 2 + -4x + 4x2 = -2 + 2 + 6x + -6x + -1x2 + x2 Combine like terms: -2 + 2 = 0 2 + -4x + 4x2 = 0 + 6x + -6x + -1x2 + x2 2 + -4x + 4x2 = 6x + -6x + -1x2 + x2 Combine like terms: 6x + -6x = 0 2 + -4x + 4x2 = 0 + -1x2 + x2 2 + -4x + 4x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -2x + 2x2) = 0 Ignore the factor 2.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 + -1x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1x + x2 = 0 + -0.5 -1x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1x + x2 = -0.5 The x term is -1x. 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. -1x + 0.25 + x2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1x + 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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