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Simplifying 5m2 + -18m + 8 = 0 Reorder the terms: 8 + -18m + 5m2 = 0 Solving 8 + -18m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -3.6m + m2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -3.6m + -1.6 + m2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -3.6m + m2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -3.6m + m2 = 0 + -1.6 -3.6m + m2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -3.6m + m2 = -1.6 The m term is -3.6m. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6m + 3.24 + m2 = -1.6 + 3.24 Reorder the terms: 3.24 + -3.6m + m2 = -1.6 + 3.24 Combine like terms: -1.6 + 3.24 = 1.64 3.24 + -3.6m + m2 = 1.64 Factor a perfect square on the left side: (m + -1.8)(m + -1.8) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (m + -1.8) equal to 1.280624847 and -1.280624847.Subproblem 1
m + -1.8 = 1.280624847 Simplifying m + -1.8 = 1.280624847 Reorder the terms: -1.8 + m = 1.280624847 Solving -1.8 + m = 1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + m = 1.280624847 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + m = 1.280624847 + 1.8 m = 1.280624847 + 1.8 Combine like terms: 1.280624847 + 1.8 = 3.080624847 m = 3.080624847 Simplifying m = 3.080624847Subproblem 2
m + -1.8 = -1.280624847 Simplifying m + -1.8 = -1.280624847 Reorder the terms: -1.8 + m = -1.280624847 Solving -1.8 + m = -1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + m = -1.280624847 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + m = -1.280624847 + 1.8 m = -1.280624847 + 1.8 Combine like terms: -1.280624847 + 1.8 = 0.519375153 m = 0.519375153 Simplifying m = 0.519375153Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.080624847, 0.519375153}
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