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Simplifying -2x2 + -5x + 3 + -4x2 + 4x + -6 = 0 Reorder the terms: 3 + -6 + -5x + 4x + -2x2 + -4x2 = 0 Combine like terms: 3 + -6 = -3 -3 + -5x + 4x + -2x2 + -4x2 = 0 Combine like terms: -5x + 4x = -1x -3 + -1x + -2x2 + -4x2 = 0 Combine like terms: -2x2 + -4x2 = -6x2 -3 + -1x + -6x2 = 0 Solving -3 + -1x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + x + 6x2)' equal to zero and attempt to solve: Simplifying 3 + x + 6x2 = 0 Solving 3 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.1666666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.1666666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + -0.5 0.1666666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.1666666667x + x2 = -0.5 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. 0.1666666667x + 0.25 + x2 = -0.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + 0.1666666667x + 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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