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Simplifying 5m + -2m(m + 2) = -1(2m + 15) Reorder the terms: 5m + -2m(2 + m) = -1(2m + 15) 5m + (2 * -2m + m * -2m) = -1(2m + 15) 5m + (-4m + -2m2) = -1(2m + 15) Combine like terms: 5m + -4m = 1m 1m + -2m2 = -1(2m + 15) Reorder the terms: 1m + -2m2 = -1(15 + 2m) 1m + -2m2 = (15 * -1 + 2m * -1) 1m + -2m2 = (-15 + -2m) Solving 1m + -2m2 = -15 + -2m Solving for variable 'm'. Reorder the terms: 15 + 1m + 2m + -2m2 = -15 + -2m + 15 + 2m Combine like terms: 1m + 2m = 3m 15 + 3m + -2m2 = -15 + -2m + 15 + 2m Reorder the terms: 15 + 3m + -2m2 = -15 + 15 + -2m + 2m Combine like terms: -15 + 15 = 0 15 + 3m + -2m2 = 0 + -2m + 2m 15 + 3m + -2m2 = -2m + 2m Combine like terms: -2m + 2m = 0 15 + 3m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -1.5m + m2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1.5m + 7.5 + m2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1.5m + m2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1.5m + m2 = 0 + 7.5 -1.5m + m2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1.5m + m2 = 7.5 The m term is -1.5m. 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. -1.5m + 0.5625 + m2 = 7.5 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 7.5 + 0.5625 Combine like terms: 7.5 + 0.5625 = 8.0625 0.5625 + -1.5m + m2 = 8.0625 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (m + -0.75) equal to 2.839454173 and -2.839454173.Subproblem 1
m + -0.75 = 2.839454173 Simplifying m + -0.75 = 2.839454173 Reorder the terms: -0.75 + m = 2.839454173 Solving -0.75 + m = 2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 2.839454173 + 0.75 m = 2.839454173 + 0.75 Combine like terms: 2.839454173 + 0.75 = 3.589454173 m = 3.589454173 Simplifying m = 3.589454173Subproblem 2
m + -0.75 = -2.839454173 Simplifying m + -0.75 = -2.839454173 Reorder the terms: -0.75 + m = -2.839454173 Solving -0.75 + m = -2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -2.839454173 + 0.75 m = -2.839454173 + 0.75 Combine like terms: -2.839454173 + 0.75 = -2.089454173 m = -2.089454173 Simplifying m = -2.089454173Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.589454173, -2.089454173}
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