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Simplifying -4M(M + 3) = -1(2M + 15) Reorder the terms: -4M(3 + M) = -1(2M + 15) (3 * -4M + M * -4M) = -1(2M + 15) (-12M + -4M2) = -1(2M + 15) Reorder the terms: -12M + -4M2 = -1(15 + 2M) -12M + -4M2 = (15 * -1 + 2M * -1) -12M + -4M2 = (-15 + -2M) Solving -12M + -4M2 = -15 + -2M Solving for variable 'M'. Reorder the terms: 15 + -12M + 2M + -4M2 = -15 + -2M + 15 + 2M Combine like terms: -12M + 2M = -10M 15 + -10M + -4M2 = -15 + -2M + 15 + 2M Reorder the terms: 15 + -10M + -4M2 = -15 + 15 + -2M + 2M Combine like terms: -15 + 15 = 0 15 + -10M + -4M2 = 0 + -2M + 2M 15 + -10M + -4M2 = -2M + 2M Combine like terms: -2M + 2M = 0 15 + -10M + -4M2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + 2.5M + M2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2.5M + 3.75 + M2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2.5M + M2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2.5M + M2 = 0 + 3.75 2.5M + M2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2.5M + M2 = 3.75 The M term is 2.5M. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5M + 1.5625 + M2 = 3.75 + 1.5625 Reorder the terms: 1.5625 + 2.5M + M2 = 3.75 + 1.5625 Combine like terms: 3.75 + 1.5625 = 5.3125 1.5625 + 2.5M + M2 = 5.3125 Factor a perfect square on the left side: (M + 1.25)(M + 1.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (M + 1.25) equal to 2.304886114 and -2.304886114.Subproblem 1
M + 1.25 = 2.304886114 Simplifying M + 1.25 = 2.304886114 Reorder the terms: 1.25 + M = 2.304886114 Solving 1.25 + M = 2.304886114 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + M = 2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + M = 2.304886114 + -1.25 M = 2.304886114 + -1.25 Combine like terms: 2.304886114 + -1.25 = 1.054886114 M = 1.054886114 Simplifying M = 1.054886114Subproblem 2
M + 1.25 = -2.304886114 Simplifying M + 1.25 = -2.304886114 Reorder the terms: 1.25 + M = -2.304886114 Solving 1.25 + M = -2.304886114 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + M = -2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + M = -2.304886114 + -1.25 M = -2.304886114 + -1.25 Combine like terms: -2.304886114 + -1.25 = -3.554886114 M = -3.554886114 Simplifying M = -3.554886114Solution
The solution to the problem is based on the solutions from the subproblems. M = {1.054886114, -3.554886114}
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