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Simplifying m2 + -2m + 1 = 44 Reorder the terms: 1 + -2m + m2 = 44 Solving 1 + -2m + m2 = 44 Solving for variable 'm'. Reorder the terms: 1 + -44 + -2m + m2 = 44 + -44 Combine like terms: 1 + -44 = -43 -43 + -2m + m2 = 44 + -44 Combine like terms: 44 + -44 = 0 -43 + -2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -2m + 43 + m2 = 0 + 43 Reorder the terms: -43 + 43 + -2m + m2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -2m + m2 = 0 + 43 -2m + m2 = 0 + 43 Combine like terms: 0 + 43 = 43 -2m + m2 = 43 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 = 43 + 1 Reorder the terms: 1 + -2m + m2 = 43 + 1 Combine like terms: 43 + 1 = 44 1 + -2m + m2 = 44 Factor a perfect square on the left side: (m + -1)(m + -1) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (m + -1) equal to 6.633249581 and -6.633249581.Subproblem 1
m + -1 = 6.633249581 Simplifying m + -1 = 6.633249581 Reorder the terms: -1 + m = 6.633249581 Solving -1 + m = 6.633249581 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 = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + m = 6.633249581 + 1 m = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 m = 7.633249581 Simplifying m = 7.633249581Subproblem 2
m + -1 = -6.633249581 Simplifying m + -1 = -6.633249581 Reorder the terms: -1 + m = -6.633249581 Solving -1 + m = -6.633249581 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 = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + m = -6.633249581 + 1 m = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 m = -5.633249581 Simplifying m = -5.633249581Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.633249581, -5.633249581}
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