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Simplifying m2 + -17m + -77 = 0 Reorder the terms: -77 + -17m + m2 = 0 Solving -77 + -17m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -17m + 77 + m2 = 0 + 77 Reorder the terms: -77 + 77 + -17m + m2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -17m + m2 = 0 + 77 -17m + m2 = 0 + 77 Combine like terms: 0 + 77 = 77 -17m + m2 = 77 The m term is -17m. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17m + 72.25 + m2 = 77 + 72.25 Reorder the terms: 72.25 + -17m + m2 = 77 + 72.25 Combine like terms: 77 + 72.25 = 149.25 72.25 + -17m + m2 = 149.25 Factor a perfect square on the left side: (m + -8.5)(m + -8.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (m + -8.5) equal to 12.216791723 and -12.216791723.Subproblem 1
m + -8.5 = 12.216791723 Simplifying m + -8.5 = 12.216791723 Reorder the terms: -8.5 + m = 12.216791723 Solving -8.5 + m = 12.216791723 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + m = 12.216791723 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = 12.216791723 + 8.5 m = 12.216791723 + 8.5 Combine like terms: 12.216791723 + 8.5 = 20.716791723 m = 20.716791723 Simplifying m = 20.716791723Subproblem 2
m + -8.5 = -12.216791723 Simplifying m + -8.5 = -12.216791723 Reorder the terms: -8.5 + m = -12.216791723 Solving -8.5 + m = -12.216791723 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + m = -12.216791723 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + m = -12.216791723 + 8.5 m = -12.216791723 + 8.5 Combine like terms: -12.216791723 + 8.5 = -3.716791723 m = -3.716791723 Simplifying m = -3.716791723Solution
The solution to the problem is based on the solutions from the subproblems. m = {20.716791723, -3.716791723}
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