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Simplifying m2 + -18m = 17 Reorder the terms: -18m + m2 = 17 Solving -18m + m2 = 17 Solving for variable 'm'. Reorder the terms: -17 + -18m + m2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -18m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -18m + 17 + m2 = 0 + 17 Reorder the terms: -17 + 17 + -18m + m2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -18m + m2 = 0 + 17 -18m + m2 = 0 + 17 Combine like terms: 0 + 17 = 17 -18m + m2 = 17 The m term is -18m. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18m + 81 + m2 = 17 + 81 Reorder the terms: 81 + -18m + m2 = 17 + 81 Combine like terms: 17 + 81 = 98 81 + -18m + m2 = 98 Factor a perfect square on the left side: (m + -9)(m + -9) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (m + -9) equal to 9.899494937 and -9.899494937.Subproblem 1
m + -9 = 9.899494937 Simplifying m + -9 = 9.899494937 Reorder the terms: -9 + m = 9.899494937 Solving -9 + m = 9.899494937 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m = 9.899494937 + 9 Combine like terms: -9 + 9 = 0 0 + m = 9.899494937 + 9 m = 9.899494937 + 9 Combine like terms: 9.899494937 + 9 = 18.899494937 m = 18.899494937 Simplifying m = 18.899494937Subproblem 2
m + -9 = -9.899494937 Simplifying m + -9 = -9.899494937 Reorder the terms: -9 + m = -9.899494937 Solving -9 + m = -9.899494937 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m = -9.899494937 + 9 Combine like terms: -9 + 9 = 0 0 + m = -9.899494937 + 9 m = -9.899494937 + 9 Combine like terms: -9.899494937 + 9 = -0.899494937 m = -0.899494937 Simplifying m = -0.899494937Solution
The solution to the problem is based on the solutions from the subproblems. m = {18.899494937, -0.899494937}
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