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Simplifying 0.9999x2 + 91.9337x = 93465.8 Reorder the terms: 91.9337x + 0.9999x2 = 93465.8 Solving 91.9337x + 0.9999x2 = 93465.8 Solving for variable 'x'. Reorder the terms: -93465.8 + 91.9337x + 0.9999x2 = 93465.8 + -93465.8 Combine like terms: 93465.8 + -93465.8 = 0.0 -93465.8 + 91.9337x + 0.9999x2 = 0.0 Begin completing the square. Divide all terms by 0.9999 the coefficient of the squared term: Divide each side by '0.9999'. -93475.14751 + 91.94289429x + x2 = 0 Move the constant term to the right: Add '93475.14751' to each side of the equation. -93475.14751 + 91.94289429x + 93475.14751 + x2 = 0 + 93475.14751 Reorder the terms: -93475.14751 + 93475.14751 + 91.94289429x + x2 = 0 + 93475.14751 Combine like terms: -93475.14751 + 93475.14751 = 0.00000 0.00000 + 91.94289429x + x2 = 0 + 93475.14751 91.94289429x + x2 = 0 + 93475.14751 Combine like terms: 0 + 93475.14751 = 93475.14751 91.94289429x + x2 = 93475.14751 The x term is 91.94289429x. Take half its coefficient (45.97144715). Square it (2113.373953) and add it to both sides. Add '2113.373953' to each side of the equation. 91.94289429x + 2113.373953 + x2 = 93475.14751 + 2113.373953 Reorder the terms: 2113.373953 + 91.94289429x + x2 = 93475.14751 + 2113.373953 Combine like terms: 93475.14751 + 2113.373953 = 95588.521463 2113.373953 + 91.94289429x + x2 = 95588.521463 Factor a perfect square on the left side: (x + 45.97144715)(x + 45.97144715) = 95588.521463 Calculate the square root of the right side: 309.173933997 Break this problem into two subproblems by setting (x + 45.97144715) equal to 309.173933997 and -309.173933997.Subproblem 1
x + 45.97144715 = 309.173933997 Simplifying x + 45.97144715 = 309.173933997 Reorder the terms: 45.97144715 + x = 309.173933997 Solving 45.97144715 + x = 309.173933997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.97144715' to each side of the equation. 45.97144715 + -45.97144715 + x = 309.173933997 + -45.97144715 Combine like terms: 45.97144715 + -45.97144715 = 0.00000000 0.00000000 + x = 309.173933997 + -45.97144715 x = 309.173933997 + -45.97144715 Combine like terms: 309.173933997 + -45.97144715 = 263.202486847 x = 263.202486847 Simplifying x = 263.202486847Subproblem 2
x + 45.97144715 = -309.173933997 Simplifying x + 45.97144715 = -309.173933997 Reorder the terms: 45.97144715 + x = -309.173933997 Solving 45.97144715 + x = -309.173933997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.97144715' to each side of the equation. 45.97144715 + -45.97144715 + x = -309.173933997 + -45.97144715 Combine like terms: 45.97144715 + -45.97144715 = 0.00000000 0.00000000 + x = -309.173933997 + -45.97144715 x = -309.173933997 + -45.97144715 Combine like terms: -309.173933997 + -45.97144715 = -355.145381147 x = -355.145381147 Simplifying x = -355.145381147Solution
The solution to the problem is based on the solutions from the subproblems. x = {263.202486847, -355.145381147}
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