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Simplifying m2 + 2m + -48 = 1 Reorder the terms: -48 + 2m + m2 = 1 Solving -48 + 2m + m2 = 1 Solving for variable 'm'. Reorder the terms: -48 + -1 + 2m + m2 = 1 + -1 Combine like terms: -48 + -1 = -49 -49 + 2m + m2 = 1 + -1 Combine like terms: 1 + -1 = 0 -49 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 2m + 49 + m2 = 0 + 49 Reorder the terms: -49 + 49 + 2m + m2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 2m + m2 = 0 + 49 2m + m2 = 0 + 49 Combine like terms: 0 + 49 = 49 2m + m2 = 49 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 = 49 + 1 Reorder the terms: 1 + 2m + m2 = 49 + 1 Combine like terms: 49 + 1 = 50 1 + 2m + m2 = 50 Factor a perfect square on the left side: (m + 1)(m + 1) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (m + 1) equal to 7.071067812 and -7.071067812.Subproblem 1
m + 1 = 7.071067812 Simplifying m + 1 = 7.071067812 Reorder the terms: 1 + m = 7.071067812 Solving 1 + m = 7.071067812 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 = 7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + m = 7.071067812 + -1 m = 7.071067812 + -1 Combine like terms: 7.071067812 + -1 = 6.071067812 m = 6.071067812 Simplifying m = 6.071067812Subproblem 2
m + 1 = -7.071067812 Simplifying m + 1 = -7.071067812 Reorder the terms: 1 + m = -7.071067812 Solving 1 + m = -7.071067812 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 = -7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + m = -7.071067812 + -1 m = -7.071067812 + -1 Combine like terms: -7.071067812 + -1 = -8.071067812 m = -8.071067812 Simplifying m = -8.071067812Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.071067812, -8.071067812}
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