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Simplifying 5m2 + 2m = 11 Reorder the terms: 2m + 5m2 = 11 Solving 2m + 5m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + 2m + 5m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 2m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 0.4m + m2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.4m + 2.2 + m2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.4m + m2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.4m + m2 = 0 + 2.2 0.4m + m2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.4m + m2 = 2.2 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 = 2.2 + 0.04 Reorder the terms: 0.04 + 0.4m + m2 = 2.2 + 0.04 Combine like terms: 2.2 + 0.04 = 2.24 0.04 + 0.4m + m2 = 2.24 Factor a perfect square on the left side: (m + 0.2)(m + 0.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (m + 0.2) equal to 1.496662955 and -1.496662955.Subproblem 1
m + 0.2 = 1.496662955 Simplifying m + 0.2 = 1.496662955 Reorder the terms: 0.2 + m = 1.496662955 Solving 0.2 + m = 1.496662955 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 = 1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = 1.496662955 + -0.2 m = 1.496662955 + -0.2 Combine like terms: 1.496662955 + -0.2 = 1.296662955 m = 1.296662955 Simplifying m = 1.296662955Subproblem 2
m + 0.2 = -1.496662955 Simplifying m + 0.2 = -1.496662955 Reorder the terms: 0.2 + m = -1.496662955 Solving 0.2 + m = -1.496662955 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 = -1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + m = -1.496662955 + -0.2 m = -1.496662955 + -0.2 Combine like terms: -1.496662955 + -0.2 = -1.696662955 m = -1.696662955 Simplifying m = -1.696662955Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.296662955, -1.696662955}
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