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Simplifying 5m2 + -10m = 511 Reorder the terms: -10m + 5m2 = 511 Solving -10m + 5m2 = 511 Solving for variable 'm'. Reorder the terms: -511 + -10m + 5m2 = 511 + -511 Combine like terms: 511 + -511 = 0 -511 + -10m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -102.2 + -2m + m2 = 0 Move the constant term to the right: Add '102.2' to each side of the equation. -102.2 + -2m + 102.2 + m2 = 0 + 102.2 Reorder the terms: -102.2 + 102.2 + -2m + m2 = 0 + 102.2 Combine like terms: -102.2 + 102.2 = 0.0 0.0 + -2m + m2 = 0 + 102.2 -2m + m2 = 0 + 102.2 Combine like terms: 0 + 102.2 = 102.2 -2m + m2 = 102.2 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 102.2 + 1 Reorder the terms: 1 + -2m + m2 = 102.2 + 1 Combine like terms: 102.2 + 1 = 103.2 1 + -2m + m2 = 103.2 Factor a perfect square on the left side: (m + -1)(m + -1) = 103.2 Calculate the square root of the right side: 10.158740079 Break this problem into two subproblems by setting (m + -1) equal to 10.158740079 and -10.158740079.Subproblem 1
m + -1 = 10.158740079 Simplifying m + -1 = 10.158740079 Reorder the terms: -1 + m = 10.158740079 Solving -1 + m = 10.158740079 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 10.158740079 + 1 Combine like terms: -1 + 1 = 0 0 + m = 10.158740079 + 1 m = 10.158740079 + 1 Combine like terms: 10.158740079 + 1 = 11.158740079 m = 11.158740079 Simplifying m = 11.158740079Subproblem 2
m + -1 = -10.158740079 Simplifying m + -1 = -10.158740079 Reorder the terms: -1 + m = -10.158740079 Solving -1 + m = -10.158740079 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -10.158740079 + 1 Combine like terms: -1 + 1 = 0 0 + m = -10.158740079 + 1 m = -10.158740079 + 1 Combine like terms: -10.158740079 + 1 = -9.158740079 m = -9.158740079 Simplifying m = -9.158740079Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.158740079, -9.158740079}
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