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Simplifying 2m2 + -10m = 14 Reorder the terms: -10m + 2m2 = 14 Solving -10m + 2m2 = 14 Solving for variable 'm'. Reorder the terms: -14 + -10m + 2m2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -10m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -5m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -5m + m2)' equal to zero and attempt to solve: Simplifying -7 + -5m + m2 = 0 Solving -7 + -5m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -5m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -5m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5m + m2 = 0 + 7 -5m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5m + m2 = 7 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 7 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + -5m + m2 = 13.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (m + -2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
m + -2.5 = 3.640054945 Simplifying m + -2.5 = 3.640054945 Reorder the terms: -2.5 + m = 3.640054945 Solving -2.5 + m = 3.640054945 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.640054945 + 2.5 m = 3.640054945 + 2.5 Combine like terms: 3.640054945 + 2.5 = 6.140054945 m = 6.140054945 Simplifying m = 6.140054945Subproblem 2
m + -2.5 = -3.640054945 Simplifying m + -2.5 = -3.640054945 Reorder the terms: -2.5 + m = -3.640054945 Solving -2.5 + m = -3.640054945 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.640054945 + 2.5 m = -3.640054945 + 2.5 Combine like terms: -3.640054945 + 2.5 = -1.140054945 m = -1.140054945 Simplifying m = -1.140054945Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.140054945, -1.140054945}Solution
m = {6.140054945, -1.140054945}
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