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Simplifying 5m2 + 72m = 162 Reorder the terms: 72m + 5m2 = 162 Solving 72m + 5m2 = 162 Solving for variable 'm'. Reorder the terms: -162 + 72m + 5m2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + 72m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -32.4 + 14.4m + m2 = 0 Move the constant term to the right: Add '32.4' to each side of the equation. -32.4 + 14.4m + 32.4 + m2 = 0 + 32.4 Reorder the terms: -32.4 + 32.4 + 14.4m + m2 = 0 + 32.4 Combine like terms: -32.4 + 32.4 = 0.0 0.0 + 14.4m + m2 = 0 + 32.4 14.4m + m2 = 0 + 32.4 Combine like terms: 0 + 32.4 = 32.4 14.4m + m2 = 32.4 The m term is 14.4m. Take half its coefficient (7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. 14.4m + 51.84 + m2 = 32.4 + 51.84 Reorder the terms: 51.84 + 14.4m + m2 = 32.4 + 51.84 Combine like terms: 32.4 + 51.84 = 84.24 51.84 + 14.4m + m2 = 84.24 Factor a perfect square on the left side: (m + 7.2)(m + 7.2) = 84.24 Calculate the square root of the right side: 9.178235124 Break this problem into two subproblems by setting (m + 7.2) equal to 9.178235124 and -9.178235124.Subproblem 1
m + 7.2 = 9.178235124 Simplifying m + 7.2 = 9.178235124 Reorder the terms: 7.2 + m = 9.178235124 Solving 7.2 + m = 9.178235124 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + m = 9.178235124 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + m = 9.178235124 + -7.2 m = 9.178235124 + -7.2 Combine like terms: 9.178235124 + -7.2 = 1.978235124 m = 1.978235124 Simplifying m = 1.978235124Subproblem 2
m + 7.2 = -9.178235124 Simplifying m + 7.2 = -9.178235124 Reorder the terms: 7.2 + m = -9.178235124 Solving 7.2 + m = -9.178235124 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + m = -9.178235124 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + m = -9.178235124 + -7.2 m = -9.178235124 + -7.2 Combine like terms: -9.178235124 + -7.2 = -16.378235124 m = -16.378235124 Simplifying m = -16.378235124Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.978235124, -16.378235124}
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