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Simplifying m2 + -20m + -35 = 0 Reorder the terms: -35 + -20m + m2 = 0 Solving -35 + -20m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -20m + 35 + m2 = 0 + 35 Reorder the terms: -35 + 35 + -20m + m2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -20m + m2 = 0 + 35 -20m + m2 = 0 + 35 Combine like terms: 0 + 35 = 35 -20m + m2 = 35 The m term is -20m. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20m + 100 + m2 = 35 + 100 Reorder the terms: 100 + -20m + m2 = 35 + 100 Combine like terms: 35 + 100 = 135 100 + -20m + m2 = 135 Factor a perfect square on the left side: (m + -10)(m + -10) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (m + -10) equal to 11.618950039 and -11.618950039.Subproblem 1
m + -10 = 11.618950039 Simplifying m + -10 = 11.618950039 Reorder the terms: -10 + m = 11.618950039 Solving -10 + m = 11.618950039 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = 11.618950039 + 10 Combine like terms: -10 + 10 = 0 0 + m = 11.618950039 + 10 m = 11.618950039 + 10 Combine like terms: 11.618950039 + 10 = 21.618950039 m = 21.618950039 Simplifying m = 21.618950039Subproblem 2
m + -10 = -11.618950039 Simplifying m + -10 = -11.618950039 Reorder the terms: -10 + m = -11.618950039 Solving -10 + m = -11.618950039 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = -11.618950039 + 10 Combine like terms: -10 + 10 = 0 0 + m = -11.618950039 + 10 m = -11.618950039 + 10 Combine like terms: -11.618950039 + 10 = -1.618950039 m = -1.618950039 Simplifying m = -1.618950039Solution
The solution to the problem is based on the solutions from the subproblems. m = {21.618950039, -1.618950039}
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