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Simplifying -31 + -4x(4x + -3) = 4(6x + 4) + -4 Reorder the terms: -31 + -4x(-3 + 4x) = 4(6x + 4) + -4 -31 + (-3 * -4x + 4x * -4x) = 4(6x + 4) + -4 -31 + (12x + -16x2) = 4(6x + 4) + -4 Reorder the terms: -31 + 12x + -16x2 = 4(4 + 6x) + -4 -31 + 12x + -16x2 = (4 * 4 + 6x * 4) + -4 -31 + 12x + -16x2 = (16 + 24x) + -4 Reorder the terms: -31 + 12x + -16x2 = 16 + -4 + 24x Combine like terms: 16 + -4 = 12 -31 + 12x + -16x2 = 12 + 24x Solving -31 + 12x + -16x2 = 12 + 24x Solving for variable 'x'. Reorder the terms: -31 + -12 + 12x + -24x + -16x2 = 12 + 24x + -12 + -24x Combine like terms: -31 + -12 = -43 -43 + 12x + -24x + -16x2 = 12 + 24x + -12 + -24x Combine like terms: 12x + -24x = -12x -43 + -12x + -16x2 = 12 + 24x + -12 + -24x Reorder the terms: -43 + -12x + -16x2 = 12 + -12 + 24x + -24x Combine like terms: 12 + -12 = 0 -43 + -12x + -16x2 = 0 + 24x + -24x -43 + -12x + -16x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -43 + -12x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(43 + 12x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(43 + 12x + 16x2)' equal to zero and attempt to solve: Simplifying 43 + 12x + 16x2 = 0 Solving 43 + 12x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.6875 + 0.75x + x2 = 0 Move the constant term to the right: Add '-2.6875' to each side of the equation. 2.6875 + 0.75x + -2.6875 + x2 = 0 + -2.6875 Reorder the terms: 2.6875 + -2.6875 + 0.75x + x2 = 0 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + 0.75x + x2 = 0 + -2.6875 0.75x + x2 = 0 + -2.6875 Combine like terms: 0 + -2.6875 = -2.6875 0.75x + x2 = -2.6875 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 = -2.6875 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -2.6875 + 0.140625 Combine like terms: -2.6875 + 0.140625 = -2.546875 0.140625 + 0.75x + x2 = -2.546875 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -2.546875 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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