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Simplifying 25m2 + -20m + -1 = 0 Reorder the terms: -1 + -20m + 25m2 = 0 Solving -1 + -20m + 25m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.8m + m2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.8m + 0.04 + m2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.8m + m2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.8m + m2 = 0 + 0.04 -0.8m + m2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.8m + m2 = 0.04 The m term is -0.8m. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8m + 0.16 + m2 = 0.04 + 0.16 Reorder the terms: 0.16 + -0.8m + m2 = 0.04 + 0.16 Combine like terms: 0.04 + 0.16 = 0.2 0.16 + -0.8m + m2 = 0.2 Factor a perfect square on the left side: (m + -0.4)(m + -0.4) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (m + -0.4) equal to 0.447213596 and -0.447213596.Subproblem 1
m + -0.4 = 0.447213596 Simplifying m + -0.4 = 0.447213596 Reorder the terms: -0.4 + m = 0.447213596 Solving -0.4 + m = 0.447213596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = 0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = 0.447213596 + 0.4 m = 0.447213596 + 0.4 Combine like terms: 0.447213596 + 0.4 = 0.847213596 m = 0.847213596 Simplifying m = 0.847213596Subproblem 2
m + -0.4 = -0.447213596 Simplifying m + -0.4 = -0.447213596 Reorder the terms: -0.4 + m = -0.447213596 Solving -0.4 + m = -0.447213596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = -0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = -0.447213596 + 0.4 m = -0.447213596 + 0.4 Combine like terms: -0.447213596 + 0.4 = -0.047213596 m = -0.047213596 Simplifying m = -0.047213596Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.847213596, -0.047213596}
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