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Simplifying m2 + 20m + 60 = 4 Reorder the terms: 60 + 20m + m2 = 4 Solving 60 + 20m + m2 = 4 Solving for variable 'm'. Reorder the terms: 60 + -4 + 20m + m2 = 4 + -4 Combine like terms: 60 + -4 = 56 56 + 20m + m2 = 4 + -4 Combine like terms: 4 + -4 = 0 56 + 20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 20m + -56 + m2 = 0 + -56 Reorder the terms: 56 + -56 + 20m + m2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 20m + m2 = 0 + -56 20m + m2 = 0 + -56 Combine like terms: 0 + -56 = -56 20m + m2 = -56 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 = -56 + 100 Reorder the terms: 100 + 20m + m2 = -56 + 100 Combine like terms: -56 + 100 = 44 100 + 20m + m2 = 44 Factor a perfect square on the left side: (m + 10)(m + 10) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (m + 10) equal to 6.633249581 and -6.633249581.Subproblem 1
m + 10 = 6.633249581 Simplifying m + 10 = 6.633249581 Reorder the terms: 10 + m = 6.633249581 Solving 10 + m = 6.633249581 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 = 6.633249581 + -10 Combine like terms: 10 + -10 = 0 0 + m = 6.633249581 + -10 m = 6.633249581 + -10 Combine like terms: 6.633249581 + -10 = -3.366750419 m = -3.366750419 Simplifying m = -3.366750419Subproblem 2
m + 10 = -6.633249581 Simplifying m + 10 = -6.633249581 Reorder the terms: 10 + m = -6.633249581 Solving 10 + m = -6.633249581 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 = -6.633249581 + -10 Combine like terms: 10 + -10 = 0 0 + m = -6.633249581 + -10 m = -6.633249581 + -10 Combine like terms: -6.633249581 + -10 = -16.633249581 m = -16.633249581 Simplifying m = -16.633249581Solution
The solution to the problem is based on the solutions from the subproblems. m = {-3.366750419, -16.633249581}
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