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Simplifying 4m2 + -2m + -3 = 0 Reorder the terms: -3 + -2m + 4m2 = 0 Solving -3 + -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'. -0.75 + -0.5m + m2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.5m + 0.75 + m2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.5m + m2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.5m + m2 = 0 + 0.75 -0.5m + m2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.5m + m2 = 0.75 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 = 0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5m + m2 = 0.75 + 0.0625 Combine like terms: 0.75 + 0.0625 = 0.8125 0.0625 + -0.5m + m2 = 0.8125 Factor a perfect square on the left side: (m + -0.25)(m + -0.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (m + -0.25) equal to 0.901387819 and -0.901387819.Subproblem 1
m + -0.25 = 0.901387819 Simplifying m + -0.25 = 0.901387819 Reorder the terms: -0.25 + m = 0.901387819 Solving -0.25 + m = 0.901387819 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 = 0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = 0.901387819 + 0.25 m = 0.901387819 + 0.25 Combine like terms: 0.901387819 + 0.25 = 1.151387819 m = 1.151387819 Simplifying m = 1.151387819Subproblem 2
m + -0.25 = -0.901387819 Simplifying m + -0.25 = -0.901387819 Reorder the terms: -0.25 + m = -0.901387819 Solving -0.25 + m = -0.901387819 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 = -0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = -0.901387819 + 0.25 m = -0.901387819 + 0.25 Combine like terms: -0.901387819 + 0.25 = -0.651387819 m = -0.651387819 Simplifying m = -0.651387819Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.151387819, -0.651387819}
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