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Simplifying m2 + -20m + -80 = 5 Reorder the terms: -80 + -20m + m2 = 5 Solving -80 + -20m + m2 = 5 Solving for variable 'm'. Reorder the terms: -80 + -5 + -20m + m2 = 5 + -5 Combine like terms: -80 + -5 = -85 -85 + -20m + m2 = 5 + -5 Combine like terms: 5 + -5 = 0 -85 + -20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -20m + 85 + m2 = 0 + 85 Reorder the terms: -85 + 85 + -20m + m2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -20m + m2 = 0 + 85 -20m + m2 = 0 + 85 Combine like terms: 0 + 85 = 85 -20m + m2 = 85 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 = 85 + 100 Reorder the terms: 100 + -20m + m2 = 85 + 100 Combine like terms: 85 + 100 = 185 100 + -20m + m2 = 185 Factor a perfect square on the left side: (m + -10)(m + -10) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (m + -10) equal to 13.601470509 and -13.601470509.Subproblem 1
m + -10 = 13.601470509 Simplifying m + -10 = 13.601470509 Reorder the terms: -10 + m = 13.601470509 Solving -10 + m = 13.601470509 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 = 13.601470509 + 10 Combine like terms: -10 + 10 = 0 0 + m = 13.601470509 + 10 m = 13.601470509 + 10 Combine like terms: 13.601470509 + 10 = 23.601470509 m = 23.601470509 Simplifying m = 23.601470509Subproblem 2
m + -10 = -13.601470509 Simplifying m + -10 = -13.601470509 Reorder the terms: -10 + m = -13.601470509 Solving -10 + m = -13.601470509 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 = -13.601470509 + 10 Combine like terms: -10 + 10 = 0 0 + m = -13.601470509 + 10 m = -13.601470509 + 10 Combine like terms: -13.601470509 + 10 = -3.601470509 m = -3.601470509 Simplifying m = -3.601470509Solution
The solution to the problem is based on the solutions from the subproblems. m = {23.601470509, -3.601470509}
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