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Simplifying 5M2 + 25M + -20 = 0 Reorder the terms: -20 + 25M + 5M2 = 0 Solving -20 + 25M + 5M2 = 0 Solving for variable 'M'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 5M + M2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + 5M + M2)' equal to zero and attempt to solve: Simplifying -4 + 5M + M2 = 0 Solving -4 + 5M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5M + 4 + M2 = 0 + 4 Reorder the terms: -4 + 4 + 5M + M2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5M + M2 = 0 + 4 5M + M2 = 0 + 4 Combine like terms: 0 + 4 = 4 5M + M2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + 5M + M2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5M + M2 = 10.25 Factor a perfect square on the left side: (M + 2.5)(M + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (M + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
M + 2.5 = 3.201562119 Simplifying M + 2.5 = 3.201562119 Reorder the terms: 2.5 + M = 3.201562119 Solving 2.5 + M = 3.201562119 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 = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + M = 3.201562119 + -2.5 M = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 M = 0.701562119 Simplifying M = 0.701562119Subproblem 2
M + 2.5 = -3.201562119 Simplifying M + 2.5 = -3.201562119 Reorder the terms: 2.5 + M = -3.201562119 Solving 2.5 + M = -3.201562119 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 = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + M = -3.201562119 + -2.5 M = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 M = -5.701562119 Simplifying M = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. M = {0.701562119, -5.701562119}Solution
M = {0.701562119, -5.701562119}
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