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Simplifying m2 + -28m = -5 Reorder the terms: -28m + m2 = -5 Solving -28m + m2 = -5 Solving for variable 'm'. Reorder the terms: 5 + -28m + m2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -28m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -28m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + -28m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -28m + m2 = 0 + -5 -28m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 -28m + m2 = -5 The m term is -28m. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28m + 196 + m2 = -5 + 196 Reorder the terms: 196 + -28m + m2 = -5 + 196 Combine like terms: -5 + 196 = 191 196 + -28m + m2 = 191 Factor a perfect square on the left side: (m + -14)(m + -14) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (m + -14) equal to 13.820274961 and -13.820274961.Subproblem 1
m + -14 = 13.820274961 Simplifying m + -14 = 13.820274961 Reorder the terms: -14 + m = 13.820274961 Solving -14 + m = 13.820274961 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = 13.820274961 + 14 Combine like terms: -14 + 14 = 0 0 + m = 13.820274961 + 14 m = 13.820274961 + 14 Combine like terms: 13.820274961 + 14 = 27.820274961 m = 27.820274961 Simplifying m = 27.820274961Subproblem 2
m + -14 = -13.820274961 Simplifying m + -14 = -13.820274961 Reorder the terms: -14 + m = -13.820274961 Solving -14 + m = -13.820274961 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = -13.820274961 + 14 Combine like terms: -14 + 14 = 0 0 + m = -13.820274961 + 14 m = -13.820274961 + 14 Combine like terms: -13.820274961 + 14 = 0.179725039 m = 0.179725039 Simplifying m = 0.179725039Solution
The solution to the problem is based on the solutions from the subproblems. m = {27.820274961, 0.179725039}
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