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Simplifying 3 = m2 + -2m + 1 Reorder the terms: 3 = 1 + -2m + m2 Solving 3 = 1 + -2m + m2 Solving for variable 'm'. Combine like terms: 3 + -1 = 2 2 + 2m + -1m2 = 1 + -2m + m2 + -1 + 2m + -1m2 Reorder the terms: 2 + 2m + -1m2 = 1 + -1 + -2m + 2m + m2 + -1m2 Combine like terms: 1 + -1 = 0 2 + 2m + -1m2 = 0 + -2m + 2m + m2 + -1m2 2 + 2m + -1m2 = -2m + 2m + m2 + -1m2 Combine like terms: -2m + 2m = 0 2 + 2m + -1m2 = 0 + m2 + -1m2 2 + 2m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 2 + 2m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -2m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2m + m2 = 0 + 2 -2m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2m + m2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2m + m2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2m + m2 = 3 Factor a perfect square on the left side: (m + -1)(m + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (m + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
m + -1 = 1.732050808 Simplifying m + -1 = 1.732050808 Reorder the terms: -1 + m = 1.732050808 Solving -1 + m = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.732050808 + 1 m = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 m = 2.732050808 Simplifying m = 2.732050808Subproblem 2
m + -1 = -1.732050808 Simplifying m + -1 = -1.732050808 Reorder the terms: -1 + m = -1.732050808 Solving -1 + m = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.732050808 + 1 m = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 m = -0.732050808 Simplifying m = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.732050808, -0.732050808}
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