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Simplifying m2 = 4m + -1 Reorder the terms: m2 = -1 + 4m Solving m2 = -1 + 4m Solving for variable 'm'. Reorder the terms: 1 + -4m + m2 = -1 + 4m + 1 + -4m Reorder the terms: 1 + -4m + m2 = -1 + 1 + 4m + -4m Combine like terms: -1 + 1 = 0 1 + -4m + m2 = 0 + 4m + -4m 1 + -4m + m2 = 4m + -4m Combine like terms: 4m + -4m = 0 1 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -4m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4m + m2 = 0 + -1 -4m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4m + m2 = -1 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = -1 + 4 Reorder the terms: 4 + -4m + m2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4m + m2 = 3 Factor a perfect square on the left side: (m + -2)(m + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (m + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
m + -2 = 1.732050808 Simplifying m + -2 = 1.732050808 Reorder the terms: -2 + m = 1.732050808 Solving -2 + m = 1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + m = 1.732050808 + 2 m = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 m = 3.732050808 Simplifying m = 3.732050808Subproblem 2
m + -2 = -1.732050808 Simplifying m + -2 = -1.732050808 Reorder the terms: -2 + m = -1.732050808 Solving -2 + m = -1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + m = -1.732050808 + 2 m = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 m = 0.267949192 Simplifying m = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.732050808, 0.267949192}
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