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Simplifying m2 + 2m = 26 Reorder the terms: 2m + m2 = 26 Solving 2m + m2 = 26 Solving for variable 'm'. Reorder the terms: -26 + 2m + m2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 2m + 26 + m2 = 0 + 26 Reorder the terms: -26 + 26 + 2m + m2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 2m + m2 = 0 + 26 2m + m2 = 0 + 26 Combine like terms: 0 + 26 = 26 2m + m2 = 26 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 26 + 1 Reorder the terms: 1 + 2m + m2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + 2m + m2 = 27 Factor a perfect square on the left side: (m + 1)(m + 1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (m + 1) equal to 5.196152423 and -5.196152423.Subproblem 1
m + 1 = 5.196152423 Simplifying m + 1 = 5.196152423 Reorder the terms: 1 + m = 5.196152423 Solving 1 + m = 5.196152423 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 5.196152423 + -1 Combine like terms: 1 + -1 = 0 0 + m = 5.196152423 + -1 m = 5.196152423 + -1 Combine like terms: 5.196152423 + -1 = 4.196152423 m = 4.196152423 Simplifying m = 4.196152423Subproblem 2
m + 1 = -5.196152423 Simplifying m + 1 = -5.196152423 Reorder the terms: 1 + m = -5.196152423 Solving 1 + m = -5.196152423 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -5.196152423 + -1 Combine like terms: 1 + -1 = 0 0 + m = -5.196152423 + -1 m = -5.196152423 + -1 Combine like terms: -5.196152423 + -1 = -6.196152423 m = -6.196152423 Simplifying m = -6.196152423Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.196152423, -6.196152423}
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