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Simplifying -2m + 16 = m2 Reorder the terms: 16 + -2m = m2 Solving 16 + -2m = m2 Solving for variable 'm'. Combine like terms: m2 + -1m2 = 0 16 + -2m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 2m + m2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 2m + 16 + m2 = 0 + 16 Reorder the terms: -16 + 16 + 2m + m2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2m + m2 = 0 + 16 2m + m2 = 0 + 16 Combine like terms: 0 + 16 = 16 2m + m2 = 16 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 = 16 + 1 Reorder the terms: 1 + 2m + m2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2m + m2 = 17 Factor a perfect square on the left side: (m + 1)(m + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (m + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
m + 1 = 4.123105626 Simplifying m + 1 = 4.123105626 Reorder the terms: 1 + m = 4.123105626 Solving 1 + m = 4.123105626 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 = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + m = 4.123105626 + -1 m = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 m = 3.123105626 Simplifying m = 3.123105626Subproblem 2
m + 1 = -4.123105626 Simplifying m + 1 = -4.123105626 Reorder the terms: 1 + m = -4.123105626 Solving 1 + m = -4.123105626 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 = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + m = -4.123105626 + -1 m = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 m = -5.123105626 Simplifying m = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.123105626, -5.123105626}
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