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Simplifying M(M + -10) = 210 Reorder the terms: M(-10 + M) = 210 (-10 * M + M * M) = 210 (-10M + M2) = 210 Solving -10M + M2 = 210 Solving for variable 'M'. Reorder the terms: -210 + -10M + M2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + -10M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -10M + 210 + M2 = 0 + 210 Reorder the terms: -210 + 210 + -10M + M2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -10M + M2 = 0 + 210 -10M + M2 = 0 + 210 Combine like terms: 0 + 210 = 210 -10M + M2 = 210 The M term is -10M. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10M + 25 + M2 = 210 + 25 Reorder the terms: 25 + -10M + M2 = 210 + 25 Combine like terms: 210 + 25 = 235 25 + -10M + M2 = 235 Factor a perfect square on the left side: (M + -5)(M + -5) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (M + -5) equal to 15.329709717 and -15.329709717.Subproblem 1
M + -5 = 15.329709717 Simplifying M + -5 = 15.329709717 Reorder the terms: -5 + M = 15.329709717 Solving -5 + M = 15.329709717 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + M = 15.329709717 + 5 Combine like terms: -5 + 5 = 0 0 + M = 15.329709717 + 5 M = 15.329709717 + 5 Combine like terms: 15.329709717 + 5 = 20.329709717 M = 20.329709717 Simplifying M = 20.329709717Subproblem 2
M + -5 = -15.329709717 Simplifying M + -5 = -15.329709717 Reorder the terms: -5 + M = -15.329709717 Solving -5 + M = -15.329709717 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + M = -15.329709717 + 5 Combine like terms: -5 + 5 = 0 0 + M = -15.329709717 + 5 M = -15.329709717 + 5 Combine like terms: -15.329709717 + 5 = -10.329709717 M = -10.329709717 Simplifying M = -10.329709717Solution
The solution to the problem is based on the solutions from the subproblems. M = {20.329709717, -10.329709717}
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