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Simplifying 4160 = 3.026x2 + 377.7x Reorder the terms: 4160 = 377.7x + 3.026x2 Solving 4160 = 377.7x + 3.026x2 Solving for variable 'x'. Reorder the terms: 4160 + -377.7x + -3.026x2 = 377.7x + -377.7x + 3.026x2 + -3.026x2 Combine like terms: 377.7x + -377.7x = 0.0 4160 + -377.7x + -3.026x2 = 0.0 + 3.026x2 + -3.026x2 4160 + -377.7x + -3.026x2 = 3.026x2 + -3.026x2 Combine like terms: 3.026x2 + -3.026x2 = 0.000 4160 + -377.7x + -3.026x2 = 0.000 Begin completing the square. Divide all terms by -3.026 the coefficient of the squared term: Divide each side by '-3.026'. -1374.752148 + 124.8182419x + x2 = 0 Move the constant term to the right: Add '1374.752148' to each side of the equation. -1374.752148 + 124.8182419x + 1374.752148 + x2 = 0 + 1374.752148 Reorder the terms: -1374.752148 + 1374.752148 + 124.8182419x + x2 = 0 + 1374.752148 Combine like terms: -1374.752148 + 1374.752148 = 0.000000 0.000000 + 124.8182419x + x2 = 0 + 1374.752148 124.8182419x + x2 = 0 + 1374.752148 Combine like terms: 0 + 1374.752148 = 1374.752148 124.8182419x + x2 = 1374.752148 The x term is 124.8182419x. Take half its coefficient (62.40912095). Square it (3894.898378) and add it to both sides. Add '3894.898378' to each side of the equation. 124.8182419x + 3894.898378 + x2 = 1374.752148 + 3894.898378 Reorder the terms: 3894.898378 + 124.8182419x + x2 = 1374.752148 + 3894.898378 Combine like terms: 1374.752148 + 3894.898378 = 5269.650526 3894.898378 + 124.8182419x + x2 = 5269.650526 Factor a perfect square on the left side: (x + 62.40912095)(x + 62.40912095) = 5269.650526 Calculate the square root of the right side: 72.592358592 Break this problem into two subproblems by setting (x + 62.40912095) equal to 72.592358592 and -72.592358592.Subproblem 1
x + 62.40912095 = 72.592358592 Simplifying x + 62.40912095 = 72.592358592 Reorder the terms: 62.40912095 + x = 72.592358592 Solving 62.40912095 + x = 72.592358592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.40912095' to each side of the equation. 62.40912095 + -62.40912095 + x = 72.592358592 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = 72.592358592 + -62.40912095 x = 72.592358592 + -62.40912095 Combine like terms: 72.592358592 + -62.40912095 = 10.183237642 x = 10.183237642 Simplifying x = 10.183237642Subproblem 2
x + 62.40912095 = -72.592358592 Simplifying x + 62.40912095 = -72.592358592 Reorder the terms: 62.40912095 + x = -72.592358592 Solving 62.40912095 + x = -72.592358592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62.40912095' to each side of the equation. 62.40912095 + -62.40912095 + x = -72.592358592 + -62.40912095 Combine like terms: 62.40912095 + -62.40912095 = 0.00000000 0.00000000 + x = -72.592358592 + -62.40912095 x = -72.592358592 + -62.40912095 Combine like terms: -72.592358592 + -62.40912095 = -135.001479542 x = -135.001479542 Simplifying x = -135.001479542Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.183237642, -135.001479542}
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