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Simplifying 0.08616x2 + 3.1622x + -88.27 = 0 Reorder the terms: -88.27 + 3.1622x + 0.08616x2 = 0 Solving -88.27 + 3.1622x + 0.08616x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.08616 the coefficient of the squared term: Divide each side by '0.08616'. -1024.489322 + 36.70148561x + x2 = 0 Move the constant term to the right: Add '1024.489322' to each side of the equation. -1024.489322 + 36.70148561x + 1024.489322 + x2 = 0 + 1024.489322 Reorder the terms: -1024.489322 + 1024.489322 + 36.70148561x + x2 = 0 + 1024.489322 Combine like terms: -1024.489322 + 1024.489322 = 0.000000 0.000000 + 36.70148561x + x2 = 0 + 1024.489322 36.70148561x + x2 = 0 + 1024.489322 Combine like terms: 0 + 1024.489322 = 1024.489322 36.70148561x + x2 = 1024.489322 The x term is 36.70148561x. Take half its coefficient (18.35074281). Square it (336.7497617) and add it to both sides. Add '336.7497617' to each side of the equation. 36.70148561x + 336.7497617 + x2 = 1024.489322 + 336.7497617 Reorder the terms: 336.7497617 + 36.70148561x + x2 = 1024.489322 + 336.7497617 Combine like terms: 1024.489322 + 336.7497617 = 1361.2390837 336.7497617 + 36.70148561x + x2 = 1361.2390837 Factor a perfect square on the left side: (x + 18.35074281)(x + 18.35074281) = 1361.2390837 Calculate the square root of the right side: 36.894973692 Break this problem into two subproblems by setting (x + 18.35074281) equal to 36.894973692 and -36.894973692.Subproblem 1
x + 18.35074281 = 36.894973692 Simplifying x + 18.35074281 = 36.894973692 Reorder the terms: 18.35074281 + x = 36.894973692 Solving 18.35074281 + x = 36.894973692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.35074281' to each side of the equation. 18.35074281 + -18.35074281 + x = 36.894973692 + -18.35074281 Combine like terms: 18.35074281 + -18.35074281 = 0.00000000 0.00000000 + x = 36.894973692 + -18.35074281 x = 36.894973692 + -18.35074281 Combine like terms: 36.894973692 + -18.35074281 = 18.544230882 x = 18.544230882 Simplifying x = 18.544230882Subproblem 2
x + 18.35074281 = -36.894973692 Simplifying x + 18.35074281 = -36.894973692 Reorder the terms: 18.35074281 + x = -36.894973692 Solving 18.35074281 + x = -36.894973692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.35074281' to each side of the equation. 18.35074281 + -18.35074281 + x = -36.894973692 + -18.35074281 Combine like terms: 18.35074281 + -18.35074281 = 0.00000000 0.00000000 + x = -36.894973692 + -18.35074281 x = -36.894973692 + -18.35074281 Combine like terms: -36.894973692 + -18.35074281 = -55.245716502 x = -55.245716502 Simplifying x = -55.245716502Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.544230882, -55.245716502}
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