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Simplifying m2 + 30m = 17 Reorder the terms: 30m + m2 = 17 Solving 30m + m2 = 17 Solving for variable 'm'. Reorder the terms: -17 + 30m + m2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 30m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 30m + 17 + m2 = 0 + 17 Reorder the terms: -17 + 17 + 30m + m2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 30m + m2 = 0 + 17 30m + m2 = 0 + 17 Combine like terms: 0 + 17 = 17 30m + m2 = 17 The m term is 30m. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30m + 225 + m2 = 17 + 225 Reorder the terms: 225 + 30m + m2 = 17 + 225 Combine like terms: 17 + 225 = 242 225 + 30m + m2 = 242 Factor a perfect square on the left side: (m + 15)(m + 15) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (m + 15) equal to 15.556349186 and -15.556349186.Subproblem 1
m + 15 = 15.556349186 Simplifying m + 15 = 15.556349186 Reorder the terms: 15 + m = 15.556349186 Solving 15 + m = 15.556349186 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + m = 15.556349186 + -15 Combine like terms: 15 + -15 = 0 0 + m = 15.556349186 + -15 m = 15.556349186 + -15 Combine like terms: 15.556349186 + -15 = 0.556349186 m = 0.556349186 Simplifying m = 0.556349186Subproblem 2
m + 15 = -15.556349186 Simplifying m + 15 = -15.556349186 Reorder the terms: 15 + m = -15.556349186 Solving 15 + m = -15.556349186 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + m = -15.556349186 + -15 Combine like terms: 15 + -15 = 0 0 + m = -15.556349186 + -15 m = -15.556349186 + -15 Combine like terms: -15.556349186 + -15 = -30.556349186 m = -30.556349186 Simplifying m = -30.556349186Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.556349186, -30.556349186}
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