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Simplifying x2 + -3x + -46 = 5x2 + -6 Reorder the terms: -46 + -3x + x2 = 5x2 + -6 Reorder the terms: -46 + -3x + x2 = -6 + 5x2 Solving -46 + -3x + x2 = -6 + 5x2 Solving for variable 'x'. Reorder the terms: -46 + 6 + -3x + x2 + -5x2 = -6 + 5x2 + 6 + -5x2 Combine like terms: -46 + 6 = -40 -40 + -3x + x2 + -5x2 = -6 + 5x2 + 6 + -5x2 Combine like terms: x2 + -5x2 = -4x2 -40 + -3x + -4x2 = -6 + 5x2 + 6 + -5x2 Reorder the terms: -40 + -3x + -4x2 = -6 + 6 + 5x2 + -5x2 Combine like terms: -6 + 6 = 0 -40 + -3x + -4x2 = 0 + 5x2 + -5x2 -40 + -3x + -4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -40 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 40 + 3x + 4x2 = 0 Solving 40 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + 0.75x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 0.75x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 0.75x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 0.75x + x2 = 0 + -10 0.75x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 0.75x + x2 = -10 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -10 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -10 + 0.140625 Combine like terms: -10 + 0.140625 = -9.859375 0.140625 + 0.75x + x2 = -9.859375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -9.859375 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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