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Simplifying m2 + -14m = 58 Reorder the terms: -14m + m2 = 58 Solving -14m + m2 = 58 Solving for variable 'm'. Reorder the terms: -58 + -14m + m2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -14m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -14m + 58 + m2 = 0 + 58 Reorder the terms: -58 + 58 + -14m + m2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -14m + m2 = 0 + 58 -14m + m2 = 0 + 58 Combine like terms: 0 + 58 = 58 -14m + m2 = 58 The m term is -14m. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14m + 49 + m2 = 58 + 49 Reorder the terms: 49 + -14m + m2 = 58 + 49 Combine like terms: 58 + 49 = 107 49 + -14m + m2 = 107 Factor a perfect square on the left side: (m + -7)(m + -7) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (m + -7) equal to 10.344080433 and -10.344080433.Subproblem 1
m + -7 = 10.344080433 Simplifying m + -7 = 10.344080433 Reorder the terms: -7 + m = 10.344080433 Solving -7 + m = 10.344080433 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = 10.344080433 + 7 Combine like terms: -7 + 7 = 0 0 + m = 10.344080433 + 7 m = 10.344080433 + 7 Combine like terms: 10.344080433 + 7 = 17.344080433 m = 17.344080433 Simplifying m = 17.344080433Subproblem 2
m + -7 = -10.344080433 Simplifying m + -7 = -10.344080433 Reorder the terms: -7 + m = -10.344080433 Solving -7 + m = -10.344080433 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = -10.344080433 + 7 Combine like terms: -7 + 7 = 0 0 + m = -10.344080433 + 7 m = -10.344080433 + 7 Combine like terms: -10.344080433 + 7 = -3.344080433 m = -3.344080433 Simplifying m = -3.344080433Solution
The solution to the problem is based on the solutions from the subproblems. m = {17.344080433, -3.344080433}
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