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Simplifying m2 + -24m + -37 = 0 Reorder the terms: -37 + -24m + m2 = 0 Solving -37 + -24m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -24m + 37 + m2 = 0 + 37 Reorder the terms: -37 + 37 + -24m + m2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -24m + m2 = 0 + 37 -24m + m2 = 0 + 37 Combine like terms: 0 + 37 = 37 -24m + m2 = 37 The m term is -24m. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24m + 144 + m2 = 37 + 144 Reorder the terms: 144 + -24m + m2 = 37 + 144 Combine like terms: 37 + 144 = 181 144 + -24m + m2 = 181 Factor a perfect square on the left side: (m + -12)(m + -12) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (m + -12) equal to 13.453624047 and -13.453624047.Subproblem 1
m + -12 = 13.453624047 Simplifying m + -12 = 13.453624047 Reorder the terms: -12 + m = 13.453624047 Solving -12 + m = 13.453624047 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + m = 13.453624047 + 12 Combine like terms: -12 + 12 = 0 0 + m = 13.453624047 + 12 m = 13.453624047 + 12 Combine like terms: 13.453624047 + 12 = 25.453624047 m = 25.453624047 Simplifying m = 25.453624047Subproblem 2
m + -12 = -13.453624047 Simplifying m + -12 = -13.453624047 Reorder the terms: -12 + m = -13.453624047 Solving -12 + m = -13.453624047 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + m = -13.453624047 + 12 Combine like terms: -12 + 12 = 0 0 + m = -13.453624047 + 12 m = -13.453624047 + 12 Combine like terms: -13.453624047 + 12 = -1.453624047 m = -1.453624047 Simplifying m = -1.453624047Solution
The solution to the problem is based on the solutions from the subproblems. m = {25.453624047, -1.453624047}
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