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Simplifying 2m2 + -20m + -13 = 0 Reorder the terms: -13 + -20m + 2m2 = 0 Solving -13 + -20m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -10m + m2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -10m + 6.5 + m2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -10m + m2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -10m + m2 = 0 + 6.5 -10m + m2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -10m + m2 = 6.5 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = 6.5 + 25 Reorder the terms: 25 + -10m + m2 = 6.5 + 25 Combine like terms: 6.5 + 25 = 31.5 25 + -10m + m2 = 31.5 Factor a perfect square on the left side: (m + -5)(m + -5) = 31.5 Calculate the square root of the right side: 5.61248608 Break this problem into two subproblems by setting (m + -5) equal to 5.61248608 and -5.61248608.Subproblem 1
m + -5 = 5.61248608 Simplifying m + -5 = 5.61248608 Reorder the terms: -5 + m = 5.61248608 Solving -5 + m = 5.61248608 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 5.61248608 + 5 Combine like terms: -5 + 5 = 0 0 + m = 5.61248608 + 5 m = 5.61248608 + 5 Combine like terms: 5.61248608 + 5 = 10.61248608 m = 10.61248608 Simplifying m = 10.61248608Subproblem 2
m + -5 = -5.61248608 Simplifying m + -5 = -5.61248608 Reorder the terms: -5 + m = -5.61248608 Solving -5 + m = -5.61248608 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -5.61248608 + 5 Combine like terms: -5 + 5 = 0 0 + m = -5.61248608 + 5 m = -5.61248608 + 5 Combine like terms: -5.61248608 + 5 = -0.61248608 m = -0.61248608 Simplifying m = -0.61248608Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.61248608, -0.61248608}
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