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Simplifying 95000 = 3362x2 + -17270x + 24043 Reorder the terms: 95000 = 24043 + -17270x + 3362x2 Solving 95000 = 24043 + -17270x + 3362x2 Solving for variable 'x'. Combine like terms: 95000 + -24043 = 70957 70957 + 17270x + -3362x2 = 24043 + -17270x + 3362x2 + -24043 + 17270x + -3362x2 Reorder the terms: 70957 + 17270x + -3362x2 = 24043 + -24043 + -17270x + 17270x + 3362x2 + -3362x2 Combine like terms: 24043 + -24043 = 0 70957 + 17270x + -3362x2 = 0 + -17270x + 17270x + 3362x2 + -3362x2 70957 + 17270x + -3362x2 = -17270x + 17270x + 3362x2 + -3362x2 Combine like terms: -17270x + 17270x = 0 70957 + 17270x + -3362x2 = 0 + 3362x2 + -3362x2 70957 + 17270x + -3362x2 = 3362x2 + -3362x2 Combine like terms: 3362x2 + -3362x2 = 0 70957 + 17270x + -3362x2 = 0 Begin completing the square. Divide all terms by -3362 the coefficient of the squared term: Divide each side by '-3362'. -21.10559191 + -5.136823319x + x2 = 0 Move the constant term to the right: Add '21.10559191' to each side of the equation. -21.10559191 + -5.136823319x + 21.10559191 + x2 = 0 + 21.10559191 Reorder the terms: -21.10559191 + 21.10559191 + -5.136823319x + x2 = 0 + 21.10559191 Combine like terms: -21.10559191 + 21.10559191 = 0.00000000 0.00000000 + -5.136823319x + x2 = 0 + 21.10559191 -5.136823319x + x2 = 0 + 21.10559191 Combine like terms: 0 + 21.10559191 = 21.10559191 -5.136823319x + x2 = 21.10559191 The x term is -5.136823319x. Take half its coefficient (-2.56841166). Square it (6.596738455) and add it to both sides. Add '6.596738455' to each side of the equation. -5.136823319x + 6.596738455 + x2 = 21.10559191 + 6.596738455 Reorder the terms: 6.596738455 + -5.136823319x + x2 = 21.10559191 + 6.596738455 Combine like terms: 21.10559191 + 6.596738455 = 27.702330365 6.596738455 + -5.136823319x + x2 = 27.702330365 Factor a perfect square on the left side: (x + -2.56841166)(x + -2.56841166) = 27.702330365 Calculate the square root of the right side: 5.26330033 Break this problem into two subproblems by setting (x + -2.56841166) equal to 5.26330033 and -5.26330033.Subproblem 1
x + -2.56841166 = 5.26330033 Simplifying x + -2.56841166 = 5.26330033 Reorder the terms: -2.56841166 + x = 5.26330033 Solving -2.56841166 + x = 5.26330033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.56841166' to each side of the equation. -2.56841166 + 2.56841166 + x = 5.26330033 + 2.56841166 Combine like terms: -2.56841166 + 2.56841166 = 0.00000000 0.00000000 + x = 5.26330033 + 2.56841166 x = 5.26330033 + 2.56841166 Combine like terms: 5.26330033 + 2.56841166 = 7.83171199 x = 7.83171199 Simplifying x = 7.83171199Subproblem 2
x + -2.56841166 = -5.26330033 Simplifying x + -2.56841166 = -5.26330033 Reorder the terms: -2.56841166 + x = -5.26330033 Solving -2.56841166 + x = -5.26330033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.56841166' to each side of the equation. -2.56841166 + 2.56841166 + x = -5.26330033 + 2.56841166 Combine like terms: -2.56841166 + 2.56841166 = 0.00000000 0.00000000 + x = -5.26330033 + 2.56841166 x = -5.26330033 + 2.56841166 Combine like terms: -5.26330033 + 2.56841166 = -2.69488867 x = -2.69488867 Simplifying x = -2.69488867Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.83171199, -2.69488867}
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