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Simplifying -8 = 4x2 + 3x + -1 Reorder the terms: -8 = -1 + 3x + 4x2 Solving -8 = -1 + 3x + 4x2 Solving for variable 'x'. Combine like terms: -8 + 1 = -7 -7 + -3x + -4x2 = -1 + 3x + 4x2 + 1 + -3x + -4x2 Reorder the terms: -7 + -3x + -4x2 = -1 + 1 + 3x + -3x + 4x2 + -4x2 Combine like terms: -1 + 1 = 0 -7 + -3x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 -7 + -3x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 -7 + -3x + -4x2 = 0 + 4x2 + -4x2 -7 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + 4x2 = 0 Solving 7 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.75x + x2 = 0 + -1.75 0.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.75x + x2 = -1.75 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 = -1.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.75 + 0.140625 Combine like terms: -1.75 + 0.140625 = -1.609375 0.140625 + 0.75x + x2 = -1.609375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.609375 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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