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Simplifying 3.4m2 + -4.6m = 108 Reorder the terms: -4.6m + 3.4m2 = 108 Solving -4.6m + 3.4m2 = 108 Solving for variable 'm'. Reorder the terms: -108 + -4.6m + 3.4m2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -4.6m + 3.4m2 = 0 Begin completing the square. Divide all terms by 3.4 the coefficient of the squared term: Divide each side by '3.4'. -31.76470588 + -1.352941176m + m2 = 0 Move the constant term to the right: Add '31.76470588' to each side of the equation. -31.76470588 + -1.352941176m + 31.76470588 + m2 = 0 + 31.76470588 Reorder the terms: -31.76470588 + 31.76470588 + -1.352941176m + m2 = 0 + 31.76470588 Combine like terms: -31.76470588 + 31.76470588 = 0.00000000 0.00000000 + -1.352941176m + m2 = 0 + 31.76470588 -1.352941176m + m2 = 0 + 31.76470588 Combine like terms: 0 + 31.76470588 = 31.76470588 -1.352941176m + m2 = 31.76470588 The m term is -1.352941176m. Take half its coefficient (-0.676470588). Square it (0.4576124564) and add it to both sides. Add '0.4576124564' to each side of the equation. -1.352941176m + 0.4576124564 + m2 = 31.76470588 + 0.4576124564 Reorder the terms: 0.4576124564 + -1.352941176m + m2 = 31.76470588 + 0.4576124564 Combine like terms: 31.76470588 + 0.4576124564 = 32.2223183364 0.4576124564 + -1.352941176m + m2 = 32.2223183364 Factor a perfect square on the left side: (m + -0.676470588)(m + -0.676470588) = 32.2223183364 Calculate the square root of the right side: 5.676470588 Break this problem into two subproblems by setting (m + -0.676470588) equal to 5.676470588 and -5.676470588.Subproblem 1
m + -0.676470588 = 5.676470588 Simplifying m + -0.676470588 = 5.676470588 Reorder the terms: -0.676470588 + m = 5.676470588 Solving -0.676470588 + m = 5.676470588 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.676470588' to each side of the equation. -0.676470588 + 0.676470588 + m = 5.676470588 + 0.676470588 Combine like terms: -0.676470588 + 0.676470588 = 0.000000000 0.000000000 + m = 5.676470588 + 0.676470588 m = 5.676470588 + 0.676470588 Combine like terms: 5.676470588 + 0.676470588 = 6.352941176 m = 6.352941176 Simplifying m = 6.352941176Subproblem 2
m + -0.676470588 = -5.676470588 Simplifying m + -0.676470588 = -5.676470588 Reorder the terms: -0.676470588 + m = -5.676470588 Solving -0.676470588 + m = -5.676470588 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.676470588' to each side of the equation. -0.676470588 + 0.676470588 + m = -5.676470588 + 0.676470588 Combine like terms: -0.676470588 + 0.676470588 = 0.000000000 0.000000000 + m = -5.676470588 + 0.676470588 m = -5.676470588 + 0.676470588 Combine like terms: -5.676470588 + 0.676470588 = -5 m = -5 Simplifying m = -5Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.352941176, -5}
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