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Simplifying 5m2 + 2m = 8 Reorder the terms: 2m + 5m2 = 8 Solving 2m + 5m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 2m + 5m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 2m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 0.4m + m2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.4m + 1.6 + m2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.4m + m2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.4m + m2 = 0 + 1.6 0.4m + m2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.4m + m2 = 1.6 The m term is 0.4m. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4m + 0.04 + m2 = 1.6 + 0.04 Reorder the terms: 0.04 + 0.4m + m2 = 1.6 + 0.04 Combine like terms: 1.6 + 0.04 = 1.64 0.04 + 0.4m + m2 = 1.64 Factor a perfect square on the left side: (m + 0.2)(m + 0.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (m + 0.2) equal to 1.280624847 and -1.280624847.Subproblem 1
m + 0.2 = 1.280624847 Simplifying m + 0.2 = 1.280624847 Reorder the terms: 0.2 + m = 1.280624847 Solving 0.2 + m = 1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + m = 1.280624847 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = 1.280624847 + -0.2 m = 1.280624847 + -0.2 Combine like terms: 1.280624847 + -0.2 = 1.080624847 m = 1.080624847 Simplifying m = 1.080624847Subproblem 2
m + 0.2 = -1.280624847 Simplifying m + 0.2 = -1.280624847 Reorder the terms: 0.2 + m = -1.280624847 Solving 0.2 + m = -1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + m = -1.280624847 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = -1.280624847 + -0.2 m = -1.280624847 + -0.2 Combine like terms: -1.280624847 + -0.2 = -1.480624847 m = -1.480624847 Simplifying m = -1.480624847Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.080624847, -1.480624847}
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