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Simplifying 20m2 + 54m + -25 = 0 Reorder the terms: -25 + 54m + 20m2 = 0 Solving -25 + 54m + 20m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.25 + 2.7m + m2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.7m + 1.25 + m2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.7m + m2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.7m + m2 = 0 + 1.25 2.7m + m2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.7m + m2 = 1.25 The m term is 2.7m. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7m + 1.8225 + m2 = 1.25 + 1.8225 Reorder the terms: 1.8225 + 2.7m + m2 = 1.25 + 1.8225 Combine like terms: 1.25 + 1.8225 = 3.0725 1.8225 + 2.7m + m2 = 3.0725 Factor a perfect square on the left side: (m + 1.35)(m + 1.35) = 3.0725 Calculate the square root of the right side: 1.752854814 Break this problem into two subproblems by setting (m + 1.35) equal to 1.752854814 and -1.752854814.Subproblem 1
m + 1.35 = 1.752854814 Simplifying m + 1.35 = 1.752854814 Reorder the terms: 1.35 + m = 1.752854814 Solving 1.35 + m = 1.752854814 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + m = 1.752854814 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + m = 1.752854814 + -1.35 m = 1.752854814 + -1.35 Combine like terms: 1.752854814 + -1.35 = 0.402854814 m = 0.402854814 Simplifying m = 0.402854814Subproblem 2
m + 1.35 = -1.752854814 Simplifying m + 1.35 = -1.752854814 Reorder the terms: 1.35 + m = -1.752854814 Solving 1.35 + m = -1.752854814 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + m = -1.752854814 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + m = -1.752854814 + -1.35 m = -1.752854814 + -1.35 Combine like terms: -1.752854814 + -1.35 = -3.102854814 m = -3.102854814 Simplifying m = -3.102854814Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.402854814, -3.102854814}
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