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Simplifying 0 = m2 + 2m + -7 Reorder the terms: 0 = -7 + 2m + m2 Solving 0 = -7 + 2m + m2 Solving for variable 'm'. Combine like terms: 0 + 7 = 7 7 + -2m + -1m2 = -7 + 2m + m2 + 7 + -2m + -1m2 Reorder the terms: 7 + -2m + -1m2 = -7 + 7 + 2m + -2m + m2 + -1m2 Combine like terms: -7 + 7 = 0 7 + -2m + -1m2 = 0 + 2m + -2m + m2 + -1m2 7 + -2m + -1m2 = 2m + -2m + m2 + -1m2 Combine like terms: 2m + -2m = 0 7 + -2m + -1m2 = 0 + m2 + -1m2 7 + -2m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 7 + -2m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 2m + m2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + 2m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2m + m2 = 0 + 7 2m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 2m + m2 = 7 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 = 7 + 1 Reorder the terms: 1 + 2m + m2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2m + m2 = 8 Factor a perfect square on the left side: (m + 1)(m + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (m + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
m + 1 = 2.828427125 Simplifying m + 1 = 2.828427125 Reorder the terms: 1 + m = 2.828427125 Solving 1 + m = 2.828427125 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 = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.828427125 + -1 m = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 m = 1.828427125 Simplifying m = 1.828427125Subproblem 2
m + 1 = -2.828427125 Simplifying m + 1 = -2.828427125 Reorder the terms: 1 + m = -2.828427125 Solving 1 + m = -2.828427125 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 = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.828427125 + -1 m = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 m = -3.828427125 Simplifying m = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.828427125, -3.828427125}
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