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Simplifying 0.23425 = m(4 + -1m) 0.23425 = (4 * m + -1m * m) 0.23425 = (4m + -1m2) Solving 0.23425 = 4m + -1m2 Solving for variable 'm'. Reorder the terms: 0.23425 + -4m + m2 = 4m + -4m + -1m2 + m2 Combine like terms: 4m + -4m = 0 0.23425 + -4m + m2 = 0 + -1m2 + m2 0.23425 + -4m + m2 = -1m2 + m2 Combine like terms: -1m2 + m2 = 0 0.23425 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.23425' to each side of the equation. 0.23425 + -4m + -0.23425 + m2 = 0 + -0.23425 Reorder the terms: 0.23425 + -0.23425 + -4m + m2 = 0 + -0.23425 Combine like terms: 0.23425 + -0.23425 = 0.00000 0.00000 + -4m + m2 = 0 + -0.23425 -4m + m2 = 0 + -0.23425 Combine like terms: 0 + -0.23425 = -0.23425 -4m + m2 = -0.23425 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 = -0.23425 + 4 Reorder the terms: 4 + -4m + m2 = -0.23425 + 4 Combine like terms: -0.23425 + 4 = 3.76575 4 + -4m + m2 = 3.76575 Factor a perfect square on the left side: (m + -2)(m + -2) = 3.76575 Calculate the square root of the right side: 1.940554045 Break this problem into two subproblems by setting (m + -2) equal to 1.940554045 and -1.940554045.Subproblem 1
m + -2 = 1.940554045 Simplifying m + -2 = 1.940554045 Reorder the terms: -2 + m = 1.940554045 Solving -2 + m = 1.940554045 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 = 1.940554045 + 2 Combine like terms: -2 + 2 = 0 0 + m = 1.940554045 + 2 m = 1.940554045 + 2 Combine like terms: 1.940554045 + 2 = 3.940554045 m = 3.940554045 Simplifying m = 3.940554045Subproblem 2
m + -2 = -1.940554045 Simplifying m + -2 = -1.940554045 Reorder the terms: -2 + m = -1.940554045 Solving -2 + m = -1.940554045 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 = -1.940554045 + 2 Combine like terms: -2 + 2 = 0 0 + m = -1.940554045 + 2 m = -1.940554045 + 2 Combine like terms: -1.940554045 + 2 = 0.059445955 m = 0.059445955 Simplifying m = 0.059445955Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.940554045, 0.059445955}
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