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Simplifying 4m2 + 2m + -25 = 0 Reorder the terms: -25 + 2m + 4m2 = 0 Solving -25 + 2m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 0.5m + m2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.5m + 6.25 + m2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.5m + m2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.5m + m2 = 0 + 6.25 0.5m + m2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.5m + m2 = 6.25 The m term is 0.5m. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5m + 0.0625 + m2 = 6.25 + 0.0625 Reorder the terms: 0.0625 + 0.5m + m2 = 6.25 + 0.0625 Combine like terms: 6.25 + 0.0625 = 6.3125 0.0625 + 0.5m + m2 = 6.3125 Factor a perfect square on the left side: (m + 0.25)(m + 0.25) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (m + 0.25) equal to 2.512468905 and -2.512468905.Subproblem 1
m + 0.25 = 2.512468905 Simplifying m + 0.25 = 2.512468905 Reorder the terms: 0.25 + m = 2.512468905 Solving 0.25 + m = 2.512468905 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = 2.512468905 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = 2.512468905 + -0.25 m = 2.512468905 + -0.25 Combine like terms: 2.512468905 + -0.25 = 2.262468905 m = 2.262468905 Simplifying m = 2.262468905Subproblem 2
m + 0.25 = -2.512468905 Simplifying m + 0.25 = -2.512468905 Reorder the terms: 0.25 + m = -2.512468905 Solving 0.25 + m = -2.512468905 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = -2.512468905 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = -2.512468905 + -0.25 m = -2.512468905 + -0.25 Combine like terms: -2.512468905 + -0.25 = -2.762468905 m = -2.762468905 Simplifying m = -2.762468905Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.262468905, -2.762468905}
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