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Simplifying 3(1.5 + x) * 4x = -8 Reorder the terms for easier multiplication: 3 * 4x(1.5 + x) = -8 Multiply 3 * 4 12x(1.5 + x) = -8 (1.5 * 12x + x * 12x) = -8 (18x + 12x2) = -8 Solving 18x + 12x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + 18x + 12x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 18x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 9x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + 6x2 = 0 Solving 4 + 9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 1.5x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 1.5x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 1.5x + x2 = 0 + -0.6666666667 1.5x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 1.5x + x2 = -0.6666666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -0.6666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.6666666667 + 0.5625 Combine like terms: -0.6666666667 + 0.5625 = -0.1041666667 0.5625 + 1.5x + x2 = -0.1041666667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.1041666667 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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