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Simplifying 5m2 + -1m = 5 Reorder the terms: -1m + 5m2 = 5 Solving -1m + 5m2 = 5 Solving for variable 'm'. Reorder the terms: -5 + -1m + 5m2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -1m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.2m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.2m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2m + m2 = 0 + 1 -0.2m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2m + m2 = 1 The m term is -0.2m. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2m + 0.01 + m2 = 1 + 0.01 Reorder the terms: 0.01 + -0.2m + m2 = 1 + 0.01 Combine like terms: 1 + 0.01 = 1.01 0.01 + -0.2m + m2 = 1.01 Factor a perfect square on the left side: (m + -0.1)(m + -0.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (m + -0.1) equal to 1.004987562 and -1.004987562.Subproblem 1
m + -0.1 = 1.004987562 Simplifying m + -0.1 = 1.004987562 Reorder the terms: -0.1 + m = 1.004987562 Solving -0.1 + m = 1.004987562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + m = 1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = 1.004987562 + 0.1 m = 1.004987562 + 0.1 Combine like terms: 1.004987562 + 0.1 = 1.104987562 m = 1.104987562 Simplifying m = 1.104987562Subproblem 2
m + -0.1 = -1.004987562 Simplifying m + -0.1 = -1.004987562 Reorder the terms: -0.1 + m = -1.004987562 Solving -0.1 + m = -1.004987562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + m = -1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = -1.004987562 + 0.1 m = -1.004987562 + 0.1 Combine like terms: -1.004987562 + 0.1 = -0.904987562 m = -0.904987562 Simplifying m = -0.904987562Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.104987562, -0.904987562}
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