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Simplifying 5m2 + -11m + -13 = 0 Reorder the terms: -13 + -11m + 5m2 = 0 Solving -13 + -11m + 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'. -2.6 + -2.2m + m2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -2.2m + 2.6 + m2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -2.2m + m2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -2.2m + m2 = 0 + 2.6 -2.2m + m2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -2.2m + m2 = 2.6 The m term is -2.2m. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2m + 1.21 + m2 = 2.6 + 1.21 Reorder the terms: 1.21 + -2.2m + m2 = 2.6 + 1.21 Combine like terms: 2.6 + 1.21 = 3.81 1.21 + -2.2m + m2 = 3.81 Factor a perfect square on the left side: (m + -1.1)(m + -1.1) = 3.81 Calculate the square root of the right side: 1.95192213 Break this problem into two subproblems by setting (m + -1.1) equal to 1.95192213 and -1.95192213.Subproblem 1
m + -1.1 = 1.95192213 Simplifying m + -1.1 = 1.95192213 Reorder the terms: -1.1 + m = 1.95192213 Solving -1.1 + m = 1.95192213 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + m = 1.95192213 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + m = 1.95192213 + 1.1 m = 1.95192213 + 1.1 Combine like terms: 1.95192213 + 1.1 = 3.05192213 m = 3.05192213 Simplifying m = 3.05192213Subproblem 2
m + -1.1 = -1.95192213 Simplifying m + -1.1 = -1.95192213 Reorder the terms: -1.1 + m = -1.95192213 Solving -1.1 + m = -1.95192213 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + m = -1.95192213 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + m = -1.95192213 + 1.1 m = -1.95192213 + 1.1 Combine like terms: -1.95192213 + 1.1 = -0.85192213 m = -0.85192213 Simplifying m = -0.85192213Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.05192213, -0.85192213}
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