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Simplifying 91x2 + 2367x + -4 = 3849020 Reorder the terms: -4 + 2367x + 91x2 = 3849020 Solving -4 + 2367x + 91x2 = 3849020 Solving for variable 'x'. Reorder the terms: -4 + -3849020 + 2367x + 91x2 = 3849020 + -3849020 Combine like terms: -4 + -3849020 = -3849024 -3849024 + 2367x + 91x2 = 3849020 + -3849020 Combine like terms: 3849020 + -3849020 = 0 -3849024 + 2367x + 91x2 = 0 Begin completing the square. Divide all terms by 91 the coefficient of the squared term: Divide each side by '91'. -42296.96703 + 26.01098901x + x2 = 0 Move the constant term to the right: Add '42296.96703' to each side of the equation. -42296.96703 + 26.01098901x + 42296.96703 + x2 = 0 + 42296.96703 Reorder the terms: -42296.96703 + 42296.96703 + 26.01098901x + x2 = 0 + 42296.96703 Combine like terms: -42296.96703 + 42296.96703 = 0.00000 0.00000 + 26.01098901x + x2 = 0 + 42296.96703 26.01098901x + x2 = 0 + 42296.96703 Combine like terms: 0 + 42296.96703 = 42296.96703 26.01098901x + x2 = 42296.96703 The x term is 26.01098901x. Take half its coefficient (13.00549451). Square it (169.1428875) and add it to both sides. Add '169.1428875' to each side of the equation. 26.01098901x + 169.1428875 + x2 = 42296.96703 + 169.1428875 Reorder the terms: 169.1428875 + 26.01098901x + x2 = 42296.96703 + 169.1428875 Combine like terms: 42296.96703 + 169.1428875 = 42466.1099175 169.1428875 + 26.01098901x + x2 = 42466.1099175 Factor a perfect square on the left side: (x + 13.00549451)(x + 13.00549451) = 42466.1099175 Calculate the square root of the right side: 206.073069365 Break this problem into two subproblems by setting (x + 13.00549451) equal to 206.073069365 and -206.073069365.Subproblem 1
x + 13.00549451 = 206.073069365 Simplifying x + 13.00549451 = 206.073069365 Reorder the terms: 13.00549451 + x = 206.073069365 Solving 13.00549451 + x = 206.073069365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.00549451' to each side of the equation. 13.00549451 + -13.00549451 + x = 206.073069365 + -13.00549451 Combine like terms: 13.00549451 + -13.00549451 = 0.00000000 0.00000000 + x = 206.073069365 + -13.00549451 x = 206.073069365 + -13.00549451 Combine like terms: 206.073069365 + -13.00549451 = 193.067574855 x = 193.067574855 Simplifying x = 193.067574855Subproblem 2
x + 13.00549451 = -206.073069365 Simplifying x + 13.00549451 = -206.073069365 Reorder the terms: 13.00549451 + x = -206.073069365 Solving 13.00549451 + x = -206.073069365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.00549451' to each side of the equation. 13.00549451 + -13.00549451 + x = -206.073069365 + -13.00549451 Combine like terms: 13.00549451 + -13.00549451 = 0.00000000 0.00000000 + x = -206.073069365 + -13.00549451 x = -206.073069365 + -13.00549451 Combine like terms: -206.073069365 + -13.00549451 = -219.078563875 x = -219.078563875 Simplifying x = -219.078563875Solution
The solution to the problem is based on the solutions from the subproblems. x = {193.067574855, -219.078563875}
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