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Simplifying m2 + -28m = 39 Reorder the terms: -28m + m2 = 39 Solving -28m + m2 = 39 Solving for variable 'm'. Reorder the terms: -39 + -28m + m2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -28m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -28m + 39 + m2 = 0 + 39 Reorder the terms: -39 + 39 + -28m + m2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -28m + m2 = 0 + 39 -28m + m2 = 0 + 39 Combine like terms: 0 + 39 = 39 -28m + m2 = 39 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 = 39 + 196 Reorder the terms: 196 + -28m + m2 = 39 + 196 Combine like terms: 39 + 196 = 235 196 + -28m + m2 = 235 Factor a perfect square on the left side: (m + -14)(m + -14) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (m + -14) equal to 15.329709717 and -15.329709717.Subproblem 1
m + -14 = 15.329709717 Simplifying m + -14 = 15.329709717 Reorder the terms: -14 + m = 15.329709717 Solving -14 + m = 15.329709717 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 = 15.329709717 + 14 Combine like terms: -14 + 14 = 0 0 + m = 15.329709717 + 14 m = 15.329709717 + 14 Combine like terms: 15.329709717 + 14 = 29.329709717 m = 29.329709717 Simplifying m = 29.329709717Subproblem 2
m + -14 = -15.329709717 Simplifying m + -14 = -15.329709717 Reorder the terms: -14 + m = -15.329709717 Solving -14 + m = -15.329709717 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 = -15.329709717 + 14 Combine like terms: -14 + 14 = 0 0 + m = -15.329709717 + 14 m = -15.329709717 + 14 Combine like terms: -15.329709717 + 14 = -1.329709717 m = -1.329709717 Simplifying m = -1.329709717Solution
The solution to the problem is based on the solutions from the subproblems. m = {29.329709717, -1.329709717}
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