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Simplifying m2 = 10m + -5 Reorder the terms: m2 = -5 + 10m Solving m2 = -5 + 10m Solving for variable 'm'. Reorder the terms: 5 + -10m + m2 = -5 + 10m + 5 + -10m Reorder the terms: 5 + -10m + m2 = -5 + 5 + 10m + -10m Combine like terms: -5 + 5 = 0 5 + -10m + m2 = 0 + 10m + -10m 5 + -10m + m2 = 10m + -10m Combine like terms: 10m + -10m = 0 5 + -10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + -10m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10m + m2 = 0 + -5 -10m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10m + m2 = -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 = -5 + 25 Reorder the terms: 25 + -10m + m2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10m + m2 = 20 Factor a perfect square on the left side: (m + -5)(m + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (m + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
m + -5 = 4.472135955 Simplifying m + -5 = 4.472135955 Reorder the terms: -5 + m = 4.472135955 Solving -5 + m = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + m = 4.472135955 + 5 m = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 m = 9.472135955 Simplifying m = 9.472135955Subproblem 2
m + -5 = -4.472135955 Simplifying m + -5 = -4.472135955 Reorder the terms: -5 + m = -4.472135955 Solving -5 + m = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + m = -4.472135955 + 5 m = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 m = 0.527864045 Simplifying m = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.472135955, 0.527864045}
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