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Simplifying 3m2 + -15m + -22 = 0 Reorder the terms: -22 + -15m + 3m2 = 0 Solving -22 + -15m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + -5m + m2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -5m + 7.333333333 + m2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -5m + m2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -5m + m2 = 0 + 7.333333333 -5m + m2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -5m + m2 = 7.333333333 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 = 7.333333333 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 7.333333333 + 6.25 Combine like terms: 7.333333333 + 6.25 = 13.583333333 6.25 + -5m + m2 = 13.583333333 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 13.583333333 Calculate the square root of the right side: 3.685557398 Break this problem into two subproblems by setting (m + -2.5) equal to 3.685557398 and -3.685557398.Subproblem 1
m + -2.5 = 3.685557398 Simplifying m + -2.5 = 3.685557398 Reorder the terms: -2.5 + m = 3.685557398 Solving -2.5 + m = 3.685557398 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 = 3.685557398 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.685557398 + 2.5 m = 3.685557398 + 2.5 Combine like terms: 3.685557398 + 2.5 = 6.185557398 m = 6.185557398 Simplifying m = 6.185557398Subproblem 2
m + -2.5 = -3.685557398 Simplifying m + -2.5 = -3.685557398 Reorder the terms: -2.5 + m = -3.685557398 Solving -2.5 + m = -3.685557398 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 = -3.685557398 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.685557398 + 2.5 m = -3.685557398 + 2.5 Combine like terms: -3.685557398 + 2.5 = -1.185557398 m = -1.185557398 Simplifying m = -1.185557398Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.185557398, -1.185557398}
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