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Simplifying 0 = 4x2 + -2x + 6 Reorder the terms: 0 = 6 + -2x + 4x2 Solving 0 = 6 + -2x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 2x + -4x2 = 6 + -2x + 4x2 + -6 + 2x + -4x2 Reorder the terms: -6 + 2x + -4x2 = 6 + -6 + -2x + 2x + 4x2 + -4x2 Combine like terms: 6 + -6 = 0 -6 + 2x + -4x2 = 0 + -2x + 2x + 4x2 + -4x2 -6 + 2x + -4x2 = -2x + 2x + 4x2 + -4x2 Combine like terms: -2x + 2x = 0 -6 + 2x + -4x2 = 0 + 4x2 + -4x2 -6 + 2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -6 + 2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x + -2x2)' equal to zero and attempt to solve: Simplifying -3 + x + -2x2 = 0 Solving -3 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.5x + x2 = 0 + -1.5 -0.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.5x + x2 = -1.5 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. -0.5x + 0.25 + x2 = -1.5 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + -0.5x + x2 = -1.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.25 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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