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Simplifying m2 + 2m + -48 + 6 = 0 Reorder the terms: -48 + 6 + 2m + m2 = 0 Combine like terms: -48 + 6 = -42 -42 + 2m + m2 = 0 Solving -42 + 2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 2m + 42 + m2 = 0 + 42 Reorder the terms: -42 + 42 + 2m + m2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 2m + m2 = 0 + 42 2m + m2 = 0 + 42 Combine like terms: 0 + 42 = 42 2m + m2 = 42 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 = 42 + 1 Reorder the terms: 1 + 2m + m2 = 42 + 1 Combine like terms: 42 + 1 = 43 1 + 2m + m2 = 43 Factor a perfect square on the left side: (m + 1)(m + 1) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (m + 1) equal to 6.557438524 and -6.557438524.Subproblem 1
m + 1 = 6.557438524 Simplifying m + 1 = 6.557438524 Reorder the terms: 1 + m = 6.557438524 Solving 1 + m = 6.557438524 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 = 6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + m = 6.557438524 + -1 m = 6.557438524 + -1 Combine like terms: 6.557438524 + -1 = 5.557438524 m = 5.557438524 Simplifying m = 5.557438524Subproblem 2
m + 1 = -6.557438524 Simplifying m + 1 = -6.557438524 Reorder the terms: 1 + m = -6.557438524 Solving 1 + m = -6.557438524 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 = -6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + m = -6.557438524 + -1 m = -6.557438524 + -1 Combine like terms: -6.557438524 + -1 = -7.557438524 m = -7.557438524 Simplifying m = -7.557438524Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.557438524, -7.557438524}
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