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Simplifying m2 + -10m = 3 Reorder the terms: -10m + m2 = 3 Solving -10m + m2 = 3 Solving for variable 'm'. Reorder the terms: -3 + -10m + m2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -10m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -10m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10m + m2 = 0 + 3 -10m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -10m + m2 = 3 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = 3 + 25 Reorder the terms: 25 + -10m + m2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + -10m + m2 = 28 Factor a perfect square on the left side: (m + -5)(m + -5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (m + -5) equal to 5.291502622 and -5.291502622.Subproblem 1
m + -5 = 5.291502622 Simplifying m + -5 = 5.291502622 Reorder the terms: -5 + m = 5.291502622 Solving -5 + m = 5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + m = 5.291502622 + 5 m = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 m = 10.291502622 Simplifying m = 10.291502622Subproblem 2
m + -5 = -5.291502622 Simplifying m + -5 = -5.291502622 Reorder the terms: -5 + m = -5.291502622 Solving -5 + m = -5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + m = -5.291502622 + 5 m = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 m = -0.291502622 Simplifying m = -0.291502622Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.291502622, -0.291502622}
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