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Simplifying 3x + -1(2x + 4) = 2(x + 1) * 2x + 1 Reorder the terms: 3x + -1(4 + 2x) = 2(x + 1) * 2x + 1 3x + (4 * -1 + 2x * -1) = 2(x + 1) * 2x + 1 3x + (-4 + -2x) = 2(x + 1) * 2x + 1 Reorder the terms: -4 + 3x + -2x = 2(x + 1) * 2x + 1 Combine like terms: 3x + -2x = 1x -4 + 1x = 2(x + 1) * 2x + 1 Reorder the terms: -4 + 1x = 2(1 + x) * 2x + 1 Reorder the terms for easier multiplication: -4 + 1x = 2 * 2x(1 + x) + 1 Multiply 2 * 2 -4 + 1x = 4x(1 + x) + 1 -4 + 1x = (1 * 4x + x * 4x) + 1 -4 + 1x = (4x + 4x2) + 1 Reorder the terms: -4 + 1x = 1 + 4x + 4x2 Solving -4 + 1x = 1 + 4x + 4x2 Solving for variable 'x'. Reorder the terms: -4 + -1 + 1x + -4x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Combine like terms: -4 + -1 = -5 -5 + 1x + -4x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Combine like terms: 1x + -4x = -3x -5 + -3x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Reorder the terms: -5 + -3x + -4x2 = 1 + -1 + 4x + -4x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 -5 + -3x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2 -5 + -3x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 -5 + -3x + -4x2 = 0 + 4x2 + -4x2 -5 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75x + x2 = 0 + -1.25 0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75x + x2 = -1.25 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 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.109375 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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