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Simplifying 3m2 = 6m + 5 Reorder the terms: 3m2 = 5 + 6m Solving 3m2 = 5 + 6m Solving for variable 'm'. Reorder the terms: -5 + -6m + 3m2 = 5 + 6m + -5 + -6m Reorder the terms: -5 + -6m + 3m2 = 5 + -5 + 6m + -6m Combine like terms: 5 + -5 = 0 -5 + -6m + 3m2 = 0 + 6m + -6m -5 + -6m + 3m2 = 6m + -6m Combine like terms: 6m + -6m = 0 -5 + -6m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -2m + m2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2m + 1.666666667 + m2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2m + m2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2m + m2 = 0 + 1.666666667 -2m + m2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2m + m2 = 1.666666667 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 1.666666667 + 1 Reorder the terms: 1 + -2m + m2 = 1.666666667 + 1 Combine like terms: 1.666666667 + 1 = 2.666666667 1 + -2m + m2 = 2.666666667 Factor a perfect square on the left side: (m + -1)(m + -1) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (m + -1) equal to 1.632993162 and -1.632993162.Subproblem 1
m + -1 = 1.632993162 Simplifying m + -1 = 1.632993162 Reorder the terms: -1 + m = 1.632993162 Solving -1 + m = 1.632993162 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.632993162 + 1 m = 1.632993162 + 1 Combine like terms: 1.632993162 + 1 = 2.632993162 m = 2.632993162 Simplifying m = 2.632993162Subproblem 2
m + -1 = -1.632993162 Simplifying m + -1 = -1.632993162 Reorder the terms: -1 + m = -1.632993162 Solving -1 + m = -1.632993162 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.632993162 + 1 m = -1.632993162 + 1 Combine like terms: -1.632993162 + 1 = -0.632993162 m = -0.632993162 Simplifying m = -0.632993162Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.632993162, -0.632993162}
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