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Simplifying 33 = (m + -5) * m Reorder the terms: 33 = (-5 + m) * m Reorder the terms for easier multiplication: 33 = m(-5 + m) 33 = (-5 * m + m * m) 33 = (-5m + m2) Solving 33 = -5m + m2 Solving for variable 'm'. Reorder the terms: 33 + 5m + -1m2 = -5m + 5m + m2 + -1m2 Combine like terms: -5m + 5m = 0 33 + 5m + -1m2 = 0 + m2 + -1m2 33 + 5m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 33 + 5m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + -5m + m2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + -5m + 33 + m2 = 0 + 33 Reorder the terms: -33 + 33 + -5m + m2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -5m + m2 = 0 + 33 -5m + m2 = 0 + 33 Combine like terms: 0 + 33 = 33 -5m + m2 = 33 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 33 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 33 + 6.25 Combine like terms: 33 + 6.25 = 39.25 6.25 + -5m + m2 = 39.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (m + -2.5) equal to 6.264982043 and -6.264982043.Subproblem 1
m + -2.5 = 6.264982043 Simplifying m + -2.5 = 6.264982043 Reorder the terms: -2.5 + m = 6.264982043 Solving -2.5 + m = 6.264982043 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 6.264982043 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 6.264982043 + 2.5 m = 6.264982043 + 2.5 Combine like terms: 6.264982043 + 2.5 = 8.764982043 m = 8.764982043 Simplifying m = 8.764982043Subproblem 2
m + -2.5 = -6.264982043 Simplifying m + -2.5 = -6.264982043 Reorder the terms: -2.5 + m = -6.264982043 Solving -2.5 + m = -6.264982043 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -6.264982043 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -6.264982043 + 2.5 m = -6.264982043 + 2.5 Combine like terms: -6.264982043 + 2.5 = -3.764982043 m = -3.764982043 Simplifying m = -3.764982043Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.764982043, -3.764982043}
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