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Simplifying 2m2 + -17m + -26 = 0 Reorder the terms: -26 + -17m + 2m2 = 0 Solving -26 + -17m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -8.5m + m2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -8.5m + 13 + m2 = 0 + 13 Reorder the terms: -13 + 13 + -8.5m + m2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8.5m + m2 = 0 + 13 -8.5m + m2 = 0 + 13 Combine like terms: 0 + 13 = 13 -8.5m + m2 = 13 The m term is -8.5m. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5m + 18.0625 + m2 = 13 + 18.0625 Reorder the terms: 18.0625 + -8.5m + m2 = 13 + 18.0625 Combine like terms: 13 + 18.0625 = 31.0625 18.0625 + -8.5m + m2 = 31.0625 Factor a perfect square on the left side: (m + -4.25)(m + -4.25) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (m + -4.25) equal to 5.573374202 and -5.573374202.Subproblem 1
m + -4.25 = 5.573374202 Simplifying m + -4.25 = 5.573374202 Reorder the terms: -4.25 + m = 5.573374202 Solving -4.25 + m = 5.573374202 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + m = 5.573374202 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + m = 5.573374202 + 4.25 m = 5.573374202 + 4.25 Combine like terms: 5.573374202 + 4.25 = 9.823374202 m = 9.823374202 Simplifying m = 9.823374202Subproblem 2
m + -4.25 = -5.573374202 Simplifying m + -4.25 = -5.573374202 Reorder the terms: -4.25 + m = -5.573374202 Solving -4.25 + m = -5.573374202 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + m = -5.573374202 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + m = -5.573374202 + 4.25 m = -5.573374202 + 4.25 Combine like terms: -5.573374202 + 4.25 = -1.323374202 m = -1.323374202 Simplifying m = -1.323374202Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.823374202, -1.323374202}
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