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Simplifying 5m = -7m(m + 3) + 20 Reorder the terms: 5m = -7m(3 + m) + 20 5m = (3 * -7m + m * -7m) + 20 5m = (-21m + -7m2) + 20 Reorder the terms: 5m = 20 + -21m + -7m2 Solving 5m = 20 + -21m + -7m2 Solving for variable 'm'. Reorder the terms: -20 + 5m + 21m + 7m2 = 20 + -21m + -7m2 + -20 + 21m + 7m2 Combine like terms: 5m + 21m = 26m -20 + 26m + 7m2 = 20 + -21m + -7m2 + -20 + 21m + 7m2 Reorder the terms: -20 + 26m + 7m2 = 20 + -20 + -21m + 21m + -7m2 + 7m2 Combine like terms: 20 + -20 = 0 -20 + 26m + 7m2 = 0 + -21m + 21m + -7m2 + 7m2 -20 + 26m + 7m2 = -21m + 21m + -7m2 + 7m2 Combine like terms: -21m + 21m = 0 -20 + 26m + 7m2 = 0 + -7m2 + 7m2 -20 + 26m + 7m2 = -7m2 + 7m2 Combine like terms: -7m2 + 7m2 = 0 -20 + 26m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + 3.714285714m + m2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 3.714285714m + 2.857142857 + m2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 3.714285714m + m2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 3.714285714m + m2 = 0 + 2.857142857 3.714285714m + m2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 3.714285714m + m2 = 2.857142857 The m term is 3.714285714m. Take half its coefficient (1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. 3.714285714m + 3.448979591 + m2 = 2.857142857 + 3.448979591 Reorder the terms: 3.448979591 + 3.714285714m + m2 = 2.857142857 + 3.448979591 Combine like terms: 2.857142857 + 3.448979591 = 6.306122448 3.448979591 + 3.714285714m + m2 = 6.306122448 Factor a perfect square on the left side: (m + 1.857142857)(m + 1.857142857) = 6.306122448 Calculate the square root of the right side: 2.511199404 Break this problem into two subproblems by setting (m + 1.857142857) equal to 2.511199404 and -2.511199404.Subproblem 1
m + 1.857142857 = 2.511199404 Simplifying m + 1.857142857 = 2.511199404 Reorder the terms: 1.857142857 + m = 2.511199404 Solving 1.857142857 + m = 2.511199404 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + m = 2.511199404 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + m = 2.511199404 + -1.857142857 m = 2.511199404 + -1.857142857 Combine like terms: 2.511199404 + -1.857142857 = 0.654056547 m = 0.654056547 Simplifying m = 0.654056547Subproblem 2
m + 1.857142857 = -2.511199404 Simplifying m + 1.857142857 = -2.511199404 Reorder the terms: 1.857142857 + m = -2.511199404 Solving 1.857142857 + m = -2.511199404 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + m = -2.511199404 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + m = -2.511199404 + -1.857142857 m = -2.511199404 + -1.857142857 Combine like terms: -2.511199404 + -1.857142857 = -4.368342261 m = -4.368342261 Simplifying m = -4.368342261Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.654056547, -4.368342261}
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