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Simplifying 3x + -1(x + 2) + 7 = 2(x + 4) + -3x(2 + -5x) Reorder the terms: 3x + -1(2 + x) + 7 = 2(x + 4) + -3x(2 + -5x) 3x + (2 * -1 + x * -1) + 7 = 2(x + 4) + -3x(2 + -5x) 3x + (-2 + -1x) + 7 = 2(x + 4) + -3x(2 + -5x) Reorder the terms: -2 + 7 + 3x + -1x = 2(x + 4) + -3x(2 + -5x) Combine like terms: -2 + 7 = 5 5 + 3x + -1x = 2(x + 4) + -3x(2 + -5x) Combine like terms: 3x + -1x = 2x 5 + 2x = 2(x + 4) + -3x(2 + -5x) Reorder the terms: 5 + 2x = 2(4 + x) + -3x(2 + -5x) 5 + 2x = (4 * 2 + x * 2) + -3x(2 + -5x) 5 + 2x = (8 + 2x) + -3x(2 + -5x) 5 + 2x = 8 + 2x + (2 * -3x + -5x * -3x) 5 + 2x = 8 + 2x + (-6x + 15x2) Combine like terms: 2x + -6x = -4x 5 + 2x = 8 + -4x + 15x2 Solving 5 + 2x = 8 + -4x + 15x2 Solving for variable 'x'. Reorder the terms: 5 + -8 + 2x + 4x + -15x2 = 8 + -4x + 15x2 + -8 + 4x + -15x2 Combine like terms: 5 + -8 = -3 -3 + 2x + 4x + -15x2 = 8 + -4x + 15x2 + -8 + 4x + -15x2 Combine like terms: 2x + 4x = 6x -3 + 6x + -15x2 = 8 + -4x + 15x2 + -8 + 4x + -15x2 Reorder the terms: -3 + 6x + -15x2 = 8 + -8 + -4x + 4x + 15x2 + -15x2 Combine like terms: 8 + -8 = 0 -3 + 6x + -15x2 = 0 + -4x + 4x + 15x2 + -15x2 -3 + 6x + -15x2 = -4x + 4x + 15x2 + -15x2 Combine like terms: -4x + 4x = 0 -3 + 6x + -15x2 = 0 + 15x2 + -15x2 -3 + 6x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -3 + 6x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 2x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 2x + -5x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + -5x2 = 0 Solving -1 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.2 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.4x + x2 = 0 + -0.2 -0.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.4x + x2 = -0.2 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.2 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.2 + 0.04 Combine like terms: -0.2 + 0.04 = -0.16 0.04 + -0.4x + x2 = -0.16 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = -0.16 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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