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Simplifying -3(4m + 3) * 4(6m + 1) = 43 Reorder the terms: -3(3 + 4m) * 4(6m + 1) = 43 Reorder the terms: -3(3 + 4m) * 4(1 + 6m) = 43 Reorder the terms for easier multiplication: -3 * 4(3 + 4m)(1 + 6m) = 43 Multiply -3 * 4 -12(3 + 4m)(1 + 6m) = 43 Multiply (3 + 4m) * (1 + 6m) -12(3(1 + 6m) + 4m * (1 + 6m)) = 43 -12((1 * 3 + 6m * 3) + 4m * (1 + 6m)) = 43 -12((3 + 18m) + 4m * (1 + 6m)) = 43 -12(3 + 18m + (1 * 4m + 6m * 4m)) = 43 -12(3 + 18m + (4m + 24m2)) = 43 Combine like terms: 18m + 4m = 22m -12(3 + 22m + 24m2) = 43 (3 * -12 + 22m * -12 + 24m2 * -12) = 43 (-36 + -264m + -288m2) = 43 Solving -36 + -264m + -288m2 = 43 Solving for variable 'm'. Reorder the terms: -36 + -43 + -264m + -288m2 = 43 + -43 Combine like terms: -36 + -43 = -79 -79 + -264m + -288m2 = 43 + -43 Combine like terms: 43 + -43 = 0 -79 + -264m + -288m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(79 + 264m + 288m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(79 + 264m + 288m2)' equal to zero and attempt to solve: Simplifying 79 + 264m + 288m2 = 0 Solving 79 + 264m + 288m2 = 0 Begin completing the square. Divide all terms by 288 the coefficient of the squared term: Divide each side by '288'. 0.2743055556 + 0.9166666667m + m2 = 0 Move the constant term to the right: Add '-0.2743055556' to each side of the equation. 0.2743055556 + 0.9166666667m + -0.2743055556 + m2 = 0 + -0.2743055556 Reorder the terms: 0.2743055556 + -0.2743055556 + 0.9166666667m + m2 = 0 + -0.2743055556 Combine like terms: 0.2743055556 + -0.2743055556 = 0.0000000000 0.0000000000 + 0.9166666667m + m2 = 0 + -0.2743055556 0.9166666667m + m2 = 0 + -0.2743055556 Combine like terms: 0 + -0.2743055556 = -0.2743055556 0.9166666667m + m2 = -0.2743055556 The m term is 0.9166666667m. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667m + 0.2100694445 + m2 = -0.2743055556 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667m + m2 = -0.2743055556 + 0.2100694445 Combine like terms: -0.2743055556 + 0.2100694445 = -0.0642361111 0.2100694445 + 0.9166666667m + m2 = -0.0642361111 Factor a perfect square on the left side: (m + 0.4583333334)(m + 0.4583333334) = -0.0642361111 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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