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Simplifying -1[3x(2x + 5)] = -4 + -1[3(2x + -4) + -3x] Reorder the terms: -1[3x(5 + 2x)] = -4 + -1[3(2x + -4) + -3x] -1[(5 * 3x + 2x * 3x)] = -4 + -1[3(2x + -4) + -3x] -1[(15x + 6x2)] = -4 + -1[3(2x + -4) + -3x] [15x * -1 + 6x2 * -1] = -4 + -1[3(2x + -4) + -3x] [-15x + -6x2] = -4 + -1[3(2x + -4) + -3x] Reorder the terms: -15x + -6x2 = -4 + -1[3(-4 + 2x) + -3x] -15x + -6x2 = -4 + -1[(-4 * 3 + 2x * 3) + -3x] -15x + -6x2 = -4 + -1[(-12 + 6x) + -3x] Combine like terms: 6x + -3x = 3x -15x + -6x2 = -4 + -1[-12 + 3x] -15x + -6x2 = -4 + [-12 * -1 + 3x * -1] -15x + -6x2 = -4 + [12 + -3x] Combine like terms: -4 + 12 = 8 -15x + -6x2 = 8 + -3x Solving -15x + -6x2 = 8 + -3x Solving for variable 'x'. Reorder the terms: -8 + -15x + 3x + -6x2 = 8 + -3x + -8 + 3x Combine like terms: -15x + 3x = -12x -8 + -12x + -6x2 = 8 + -3x + -8 + 3x Reorder the terms: -8 + -12x + -6x2 = 8 + -8 + -3x + 3x Combine like terms: 8 + -8 = 0 -8 + -12x + -6x2 = 0 + -3x + 3x -8 + -12x + -6x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -8 + -12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 6x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + 3x2 = 0 Solving 4 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + -1.333333333 2x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2x + x2 = -1.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.333333333 + 1 Reorder the terms: 1 + 2x + x2 = -1.333333333 + 1 Combine like terms: -1.333333333 + 1 = -0.333333333 1 + 2x + x2 = -0.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.333333333 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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