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Simplifying -5m(m + -3) + 2(3m + 1) = 15 + -8 Reorder the terms: -5m(-3 + m) + 2(3m + 1) = 15 + -8 (-3 * -5m + m * -5m) + 2(3m + 1) = 15 + -8 (15m + -5m2) + 2(3m + 1) = 15 + -8 Reorder the terms: 15m + -5m2 + 2(1 + 3m) = 15 + -8 15m + -5m2 + (1 * 2 + 3m * 2) = 15 + -8 15m + -5m2 + (2 + 6m) = 15 + -8 Reorder the terms: 2 + 15m + 6m + -5m2 = 15 + -8 Combine like terms: 15m + 6m = 21m 2 + 21m + -5m2 = 15 + -8 Combine like terms: 15 + -8 = 7 2 + 21m + -5m2 = 7 Solving 2 + 21m + -5m2 = 7 Solving for variable 'm'. Reorder the terms: 2 + -7 + 21m + -5m2 = 7 + -7 Combine like terms: 2 + -7 = -5 -5 + 21m + -5m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -5 + 21m + -5m2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1 + -4.2m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.2m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -4.2m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.2m + m2 = 0 + -1 -4.2m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.2m + m2 = -1 The m term is -4.2m. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2m + 4.41 + m2 = -1 + 4.41 Reorder the terms: 4.41 + -4.2m + m2 = -1 + 4.41 Combine like terms: -1 + 4.41 = 3.41 4.41 + -4.2m + m2 = 3.41 Factor a perfect square on the left side: (m + -2.1)(m + -2.1) = 3.41 Calculate the square root of the right side: 1.846618531 Break this problem into two subproblems by setting (m + -2.1) equal to 1.846618531 and -1.846618531.Subproblem 1
m + -2.1 = 1.846618531 Simplifying m + -2.1 = 1.846618531 Reorder the terms: -2.1 + m = 1.846618531 Solving -2.1 + m = 1.846618531 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + m = 1.846618531 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + m = 1.846618531 + 2.1 m = 1.846618531 + 2.1 Combine like terms: 1.846618531 + 2.1 = 3.946618531 m = 3.946618531 Simplifying m = 3.946618531Subproblem 2
m + -2.1 = -1.846618531 Simplifying m + -2.1 = -1.846618531 Reorder the terms: -2.1 + m = -1.846618531 Solving -2.1 + m = -1.846618531 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + m = -1.846618531 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + m = -1.846618531 + 2.1 m = -1.846618531 + 2.1 Combine like terms: -1.846618531 + 2.1 = 0.253381469 m = 0.253381469 Simplifying m = 0.253381469Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.946618531, 0.253381469}
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