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Simplifying 25m2 + -75m2 + -9m + 27 = 0 Reorder the terms: 27 + -9m + 25m2 + -75m2 = 0 Combine like terms: 25m2 + -75m2 = -50m2 27 + -9m + -50m2 = 0 Solving 27 + -9m + -50m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -50 the coefficient of the squared term: Divide each side by '-50'. -0.54 + 0.18m + m2 = 0.0 Move the constant term to the right: Add '0.54' to each side of the equation. -0.54 + 0.18m + 0.54 + m2 = 0.0 + 0.54 Reorder the terms: -0.54 + 0.54 + 0.18m + m2 = 0.0 + 0.54 Combine like terms: -0.54 + 0.54 = 0.00 0.00 + 0.18m + m2 = 0.0 + 0.54 0.18m + m2 = 0.0 + 0.54 Combine like terms: 0.0 + 0.54 = 0.54 0.18m + m2 = 0.54 The m term is 0.18m. Take half its coefficient (0.09). Square it (0.0081) and add it to both sides. Add '0.0081' to each side of the equation. 0.18m + 0.0081 + m2 = 0.54 + 0.0081 Reorder the terms: 0.0081 + 0.18m + m2 = 0.54 + 0.0081 Combine like terms: 0.54 + 0.0081 = 0.5481 0.0081 + 0.18m + m2 = 0.5481 Factor a perfect square on the left side: (m + 0.09)(m + 0.09) = 0.5481 Calculate the square root of the right side: 0.740337761 Break this problem into two subproblems by setting (m + 0.09) equal to 0.740337761 and -0.740337761.Subproblem 1
m + 0.09 = 0.740337761 Simplifying m + 0.09 = 0.740337761 Reorder the terms: 0.09 + m = 0.740337761 Solving 0.09 + m = 0.740337761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + m = 0.740337761 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + m = 0.740337761 + -0.09 m = 0.740337761 + -0.09 Combine like terms: 0.740337761 + -0.09 = 0.650337761 m = 0.650337761 Simplifying m = 0.650337761Subproblem 2
m + 0.09 = -0.740337761 Simplifying m + 0.09 = -0.740337761 Reorder the terms: 0.09 + m = -0.740337761 Solving 0.09 + m = -0.740337761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + m = -0.740337761 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + m = -0.740337761 + -0.09 m = -0.740337761 + -0.09 Combine like terms: -0.740337761 + -0.09 = -0.830337761 m = -0.830337761 Simplifying m = -0.830337761Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.650337761, -0.830337761}
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