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Simplifying 88000 = 2220x2 + 5871x + 5072 Reorder the terms: 88000 = 5072 + 5871x + 2220x2 Solving 88000 = 5072 + 5871x + 2220x2 Solving for variable 'x'. Combine like terms: 88000 + -5072 = 82928 82928 + -5871x + -2220x2 = 5072 + 5871x + 2220x2 + -5072 + -5871x + -2220x2 Reorder the terms: 82928 + -5871x + -2220x2 = 5072 + -5072 + 5871x + -5871x + 2220x2 + -2220x2 Combine like terms: 5072 + -5072 = 0 82928 + -5871x + -2220x2 = 0 + 5871x + -5871x + 2220x2 + -2220x2 82928 + -5871x + -2220x2 = 5871x + -5871x + 2220x2 + -2220x2 Combine like terms: 5871x + -5871x = 0 82928 + -5871x + -2220x2 = 0 + 2220x2 + -2220x2 82928 + -5871x + -2220x2 = 2220x2 + -2220x2 Combine like terms: 2220x2 + -2220x2 = 0 82928 + -5871x + -2220x2 = 0 Begin completing the square. Divide all terms by -2220 the coefficient of the squared term: Divide each side by '-2220'. -37.35495495 + 2.644594595x + x2 = 0 Move the constant term to the right: Add '37.35495495' to each side of the equation. -37.35495495 + 2.644594595x + 37.35495495 + x2 = 0 + 37.35495495 Reorder the terms: -37.35495495 + 37.35495495 + 2.644594595x + x2 = 0 + 37.35495495 Combine like terms: -37.35495495 + 37.35495495 = 0.00000000 0.00000000 + 2.644594595x + x2 = 0 + 37.35495495 2.644594595x + x2 = 0 + 37.35495495 Combine like terms: 0 + 37.35495495 = 37.35495495 2.644594595x + x2 = 37.35495495 The x term is 2.644594595x. Take half its coefficient (1.322297298). Square it (1.748470144) and add it to both sides. Add '1.748470144' to each side of the equation. 2.644594595x + 1.748470144 + x2 = 37.35495495 + 1.748470144 Reorder the terms: 1.748470144 + 2.644594595x + x2 = 37.35495495 + 1.748470144 Combine like terms: 37.35495495 + 1.748470144 = 39.103425094 1.748470144 + 2.644594595x + x2 = 39.103425094 Factor a perfect square on the left side: (x + 1.322297298)(x + 1.322297298) = 39.103425094 Calculate the square root of the right side: 6.25327315 Break this problem into two subproblems by setting (x + 1.322297298) equal to 6.25327315 and -6.25327315.Subproblem 1
x + 1.322297298 = 6.25327315 Simplifying x + 1.322297298 = 6.25327315 Reorder the terms: 1.322297298 + x = 6.25327315 Solving 1.322297298 + x = 6.25327315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.322297298' to each side of the equation. 1.322297298 + -1.322297298 + x = 6.25327315 + -1.322297298 Combine like terms: 1.322297298 + -1.322297298 = 0.000000000 0.000000000 + x = 6.25327315 + -1.322297298 x = 6.25327315 + -1.322297298 Combine like terms: 6.25327315 + -1.322297298 = 4.930975852 x = 4.930975852 Simplifying x = 4.930975852Subproblem 2
x + 1.322297298 = -6.25327315 Simplifying x + 1.322297298 = -6.25327315 Reorder the terms: 1.322297298 + x = -6.25327315 Solving 1.322297298 + x = -6.25327315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.322297298' to each side of the equation. 1.322297298 + -1.322297298 + x = -6.25327315 + -1.322297298 Combine like terms: 1.322297298 + -1.322297298 = 0.000000000 0.000000000 + x = -6.25327315 + -1.322297298 x = -6.25327315 + -1.322297298 Combine like terms: -6.25327315 + -1.322297298 = -7.575570448 x = -7.575570448 Simplifying x = -7.575570448Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.930975852, -7.575570448}
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