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Simplifying m2 + -40m + 100 = 0 Reorder the terms: 100 + -40m + m2 = 0 Solving 100 + -40m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -40m + -100 + m2 = 0 + -100 Reorder the terms: 100 + -100 + -40m + m2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -40m + m2 = 0 + -100 -40m + m2 = 0 + -100 Combine like terms: 0 + -100 = -100 -40m + m2 = -100 The m term is -40m. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40m + 400 + m2 = -100 + 400 Reorder the terms: 400 + -40m + m2 = -100 + 400 Combine like terms: -100 + 400 = 300 400 + -40m + m2 = 300 Factor a perfect square on the left side: (m + -20)(m + -20) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (m + -20) equal to 17.320508076 and -17.320508076.Subproblem 1
m + -20 = 17.320508076 Simplifying m + -20 = 17.320508076 Reorder the terms: -20 + m = 17.320508076 Solving -20 + m = 17.320508076 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + m = 17.320508076 + 20 Combine like terms: -20 + 20 = 0 0 + m = 17.320508076 + 20 m = 17.320508076 + 20 Combine like terms: 17.320508076 + 20 = 37.320508076 m = 37.320508076 Simplifying m = 37.320508076Subproblem 2
m + -20 = -17.320508076 Simplifying m + -20 = -17.320508076 Reorder the terms: -20 + m = -17.320508076 Solving -20 + m = -17.320508076 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + m = -17.320508076 + 20 Combine like terms: -20 + 20 = 0 0 + m = -17.320508076 + 20 m = -17.320508076 + 20 Combine like terms: -17.320508076 + 20 = 2.679491924 m = 2.679491924 Simplifying m = 2.679491924Solution
The solution to the problem is based on the solutions from the subproblems. m = {37.320508076, 2.679491924}
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