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Simplifying 10m2 + -21m + -6 = 0 Reorder the terms: -6 + -21m + 10m2 = 0 Solving -6 + -21m + 10m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -2.1m + m2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -2.1m + 0.6 + m2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -2.1m + m2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -2.1m + m2 = 0 + 0.6 -2.1m + m2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -2.1m + m2 = 0.6 The m term is -2.1m. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1m + 1.1025 + m2 = 0.6 + 1.1025 Reorder the terms: 1.1025 + -2.1m + m2 = 0.6 + 1.1025 Combine like terms: 0.6 + 1.1025 = 1.7025 1.1025 + -2.1m + m2 = 1.7025 Factor a perfect square on the left side: (m + -1.05)(m + -1.05) = 1.7025 Calculate the square root of the right side: 1.304798835 Break this problem into two subproblems by setting (m + -1.05) equal to 1.304798835 and -1.304798835.Subproblem 1
m + -1.05 = 1.304798835 Simplifying m + -1.05 = 1.304798835 Reorder the terms: -1.05 + m = 1.304798835 Solving -1.05 + m = 1.304798835 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + m = 1.304798835 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + m = 1.304798835 + 1.05 m = 1.304798835 + 1.05 Combine like terms: 1.304798835 + 1.05 = 2.354798835 m = 2.354798835 Simplifying m = 2.354798835Subproblem 2
m + -1.05 = -1.304798835 Simplifying m + -1.05 = -1.304798835 Reorder the terms: -1.05 + m = -1.304798835 Solving -1.05 + m = -1.304798835 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + m = -1.304798835 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + m = -1.304798835 + 1.05 m = -1.304798835 + 1.05 Combine like terms: -1.304798835 + 1.05 = -0.254798835 m = -0.254798835 Simplifying m = -0.254798835Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.354798835, -0.254798835}
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