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Simplifying 2m2 + -14m + 3 = 0 Reorder the terms: 3 + -14m + 2m2 = 0 Solving 3 + -14m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -7m + m2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -7m + -1.5 + m2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -7m + m2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -7m + m2 = 0 + -1.5 -7m + m2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -7m + m2 = -1.5 The m term is -7m. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7m + 12.25 + m2 = -1.5 + 12.25 Reorder the terms: 12.25 + -7m + m2 = -1.5 + 12.25 Combine like terms: -1.5 + 12.25 = 10.75 12.25 + -7m + m2 = 10.75 Factor a perfect square on the left side: (m + -3.5)(m + -3.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (m + -3.5) equal to 3.278719262 and -3.278719262.Subproblem 1
m + -3.5 = 3.278719262 Simplifying m + -3.5 = 3.278719262 Reorder the terms: -3.5 + m = 3.278719262 Solving -3.5 + m = 3.278719262 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = 3.278719262 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = 3.278719262 + 3.5 m = 3.278719262 + 3.5 Combine like terms: 3.278719262 + 3.5 = 6.778719262 m = 6.778719262 Simplifying m = 6.778719262Subproblem 2
m + -3.5 = -3.278719262 Simplifying m + -3.5 = -3.278719262 Reorder the terms: -3.5 + m = -3.278719262 Solving -3.5 + m = -3.278719262 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = -3.278719262 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = -3.278719262 + 3.5 m = -3.278719262 + 3.5 Combine like terms: -3.278719262 + 3.5 = 0.221280738 m = 0.221280738 Simplifying m = 0.221280738Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.778719262, 0.221280738}
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