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Simplifying 2m2 + -19m + -1 = 0 Reorder the terms: -1 + -19m + 2m2 = 0 Solving -1 + -19m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -9.5m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -9.5m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -9.5m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -9.5m + m2 = 0 + 0.5 -9.5m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -9.5m + m2 = 0.5 The m term is -9.5m. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5m + 22.5625 + m2 = 0.5 + 22.5625 Reorder the terms: 22.5625 + -9.5m + m2 = 0.5 + 22.5625 Combine like terms: 0.5 + 22.5625 = 23.0625 22.5625 + -9.5m + m2 = 23.0625 Factor a perfect square on the left side: (m + -4.75)(m + -4.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (m + -4.75) equal to 4.802343178 and -4.802343178.Subproblem 1
m + -4.75 = 4.802343178 Simplifying m + -4.75 = 4.802343178 Reorder the terms: -4.75 + m = 4.802343178 Solving -4.75 + m = 4.802343178 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + m = 4.802343178 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + m = 4.802343178 + 4.75 m = 4.802343178 + 4.75 Combine like terms: 4.802343178 + 4.75 = 9.552343178 m = 9.552343178 Simplifying m = 9.552343178Subproblem 2
m + -4.75 = -4.802343178 Simplifying m + -4.75 = -4.802343178 Reorder the terms: -4.75 + m = -4.802343178 Solving -4.75 + m = -4.802343178 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + m = -4.802343178 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + m = -4.802343178 + 4.75 m = -4.802343178 + 4.75 Combine like terms: -4.802343178 + 4.75 = -0.052343178 m = -0.052343178 Simplifying m = -0.052343178Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.552343178, -0.052343178}
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