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Simplifying 2m2 + 6m = 22 Reorder the terms: 6m + 2m2 = 22 Solving 6m + 2m2 = 22 Solving for variable 'm'. Reorder the terms: -22 + 6m + 2m2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 6m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 3m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 3m + m2)' equal to zero and attempt to solve: Simplifying -11 + 3m + m2 = 0 Solving -11 + 3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 3m + 11 + m2 = 0 + 11 Reorder the terms: -11 + 11 + 3m + m2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3m + m2 = 0 + 11 3m + m2 = 0 + 11 Combine like terms: 0 + 11 = 11 3m + m2 = 11 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 11 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + 3m + m2 = 13.25 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (m + 1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
m + 1.5 = 3.640054945 Simplifying m + 1.5 = 3.640054945 Reorder the terms: 1.5 + m = 3.640054945 Solving 1.5 + m = 3.640054945 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 3.640054945 + -1.5 m = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 m = 2.140054945 Simplifying m = 2.140054945Subproblem 2
m + 1.5 = -3.640054945 Simplifying m + 1.5 = -3.640054945 Reorder the terms: 1.5 + m = -3.640054945 Solving 1.5 + m = -3.640054945 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -3.640054945 + -1.5 m = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 m = -5.140054945 Simplifying m = -5.140054945Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.140054945, -5.140054945}Solution
m = {2.140054945, -5.140054945}
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