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Simplifying [(7m2 + 5m + -10) + -1(5m2 + 3m + 3)] + -1(m2 + m + 2) = 0 Reorder the terms: [(-10 + 5m + 7m2) + -1(5m2 + 3m + 3)] + -1(m2 + m + 2) = 0 Remove parenthesis around (-10 + 5m + 7m2) [-10 + 5m + 7m2 + -1(5m2 + 3m + 3)] + -1(m2 + m + 2) = 0 Reorder the terms: [-10 + 5m + 7m2 + -1(3 + 3m + 5m2)] + -1(m2 + m + 2) = 0 [-10 + 5m + 7m2 + (3 * -1 + 3m * -1 + 5m2 * -1)] + -1(m2 + m + 2) = 0 [-10 + 5m + 7m2 + (-3 + -3m + -5m2)] + -1(m2 + m + 2) = 0 Reorder the terms: [-10 + -3 + 5m + -3m + 7m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: -10 + -3 = -13 [-13 + 5m + -3m + 7m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: 5m + -3m = 2m [-13 + 2m + 7m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: 7m2 + -5m2 = 2m2 [-13 + 2m + 2m2] + -1(m2 + m + 2) = 0 Remove brackets around [-13 + 2m + 2m2] -13 + 2m + 2m2 + -1(m2 + m + 2) = 0 Reorder the terms: -13 + 2m + 2m2 + -1(2 + m + m2) = 0 -13 + 2m + 2m2 + (2 * -1 + m * -1 + m2 * -1) = 0 -13 + 2m + 2m2 + (-2 + -1m + -1m2) = 0 Reorder the terms: -13 + -2 + 2m + -1m + 2m2 + -1m2 = 0 Combine like terms: -13 + -2 = -15 -15 + 2m + -1m + 2m2 + -1m2 = 0 Combine like terms: 2m + -1m = 1m -15 + 1m + 2m2 + -1m2 = 0 Combine like terms: 2m2 + -1m2 = 1m2 -15 + 1m + 1m2 = 0 Solving -15 + 1m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 1m + 15 + m2 = 0 + 15 Reorder the terms: -15 + 15 + 1m + m2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1m + m2 = 0 + 15 1m + m2 = 0 + 15 Combine like terms: 0 + 15 = 15 1m + m2 = 15 The m term is 1m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = 15 + 0.25 Reorder the terms: 0.25 + m + m2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + m + m2 = 15.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (m + 0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
m + 0.5 = 3.905124838 Simplifying m + 0.5 = 3.905124838 Reorder the terms: 0.5 + m = 3.905124838 Solving 0.5 + m = 3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 3.905124838 + -0.5 m = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 m = 3.405124838 Simplifying m = 3.405124838Subproblem 2
m + 0.5 = -3.905124838 Simplifying m + 0.5 = -3.905124838 Reorder the terms: 0.5 + m = -3.905124838 Solving 0.5 + m = -3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -3.905124838 + -0.5 m = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 m = -4.405124838 Simplifying m = -4.405124838Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.405124838, -4.405124838}
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