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Simplifying 5(1 + 3m)(71 + 8m) = -6 Multiply (1 + 3m) * (71 + 8m) 5(1(71 + 8m) + 3m * (71 + 8m)) = -6 5((71 * 1 + 8m * 1) + 3m * (71 + 8m)) = -6 5((71 + 8m) + 3m * (71 + 8m)) = -6 5(71 + 8m + (71 * 3m + 8m * 3m)) = -6 5(71 + 8m + (213m + 24m2)) = -6 Combine like terms: 8m + 213m = 221m 5(71 + 221m + 24m2) = -6 (71 * 5 + 221m * 5 + 24m2 * 5) = -6 (355 + 1105m + 120m2) = -6 Solving 355 + 1105m + 120m2 = -6 Solving for variable 'm'. Reorder the terms: 355 + 6 + 1105m + 120m2 = -6 + 6 Combine like terms: 355 + 6 = 361 361 + 1105m + 120m2 = -6 + 6 Combine like terms: -6 + 6 = 0 361 + 1105m + 120m2 = 0 Begin completing the square. Divide all terms by 120 the coefficient of the squared term: Divide each side by '120'. 3.008333333 + 9.208333333m + m2 = 0.0 Move the constant term to the right: Add '-3.008333333' to each side of the equation. 3.008333333 + 9.208333333m + -3.008333333 + m2 = 0.0 + -3.008333333 Reorder the terms: 3.008333333 + -3.008333333 + 9.208333333m + m2 = 0.0 + -3.008333333 Combine like terms: 3.008333333 + -3.008333333 = 0.000000000 0.000000000 + 9.208333333m + m2 = 0.0 + -3.008333333 9.208333333m + m2 = 0.0 + -3.008333333 Combine like terms: 0.0 + -3.008333333 = -3.008333333 9.208333333m + m2 = -3.008333333 The m term is 9.208333333m. Take half its coefficient (4.604166667). Square it (21.19835070) and add it to both sides. Add '21.19835070' to each side of the equation. 9.208333333m + 21.19835070 + m2 = -3.008333333 + 21.19835070 Reorder the terms: 21.19835070 + 9.208333333m + m2 = -3.008333333 + 21.19835070 Combine like terms: -3.008333333 + 21.19835070 = 18.190017367 21.19835070 + 9.208333333m + m2 = 18.190017367 Factor a perfect square on the left side: (m + 4.604166667)(m + 4.604166667) = 18.190017367 Calculate the square root of the right side: 4.264975658 Break this problem into two subproblems by setting (m + 4.604166667) equal to 4.264975658 and -4.264975658.Subproblem 1
m + 4.604166667 = 4.264975658 Simplifying m + 4.604166667 = 4.264975658 Reorder the terms: 4.604166667 + m = 4.264975658 Solving 4.604166667 + m = 4.264975658 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.604166667' to each side of the equation. 4.604166667 + -4.604166667 + m = 4.264975658 + -4.604166667 Combine like terms: 4.604166667 + -4.604166667 = 0.000000000 0.000000000 + m = 4.264975658 + -4.604166667 m = 4.264975658 + -4.604166667 Combine like terms: 4.264975658 + -4.604166667 = -0.339191009 m = -0.339191009 Simplifying m = -0.339191009Subproblem 2
m + 4.604166667 = -4.264975658 Simplifying m + 4.604166667 = -4.264975658 Reorder the terms: 4.604166667 + m = -4.264975658 Solving 4.604166667 + m = -4.264975658 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.604166667' to each side of the equation. 4.604166667 + -4.604166667 + m = -4.264975658 + -4.604166667 Combine like terms: 4.604166667 + -4.604166667 = 0.000000000 0.000000000 + m = -4.264975658 + -4.604166667 m = -4.264975658 + -4.604166667 Combine like terms: -4.264975658 + -4.604166667 = -8.869142325 m = -8.869142325 Simplifying m = -8.869142325Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.339191009, -8.869142325}
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