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Simplifying 150x2 + -49855.83x + -9931188.25 = 0 Reorder the terms: -9931188.25 + -49855.83x + 150x2 = 0 Solving -9931188.25 + -49855.83x + 150x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 150 the coefficient of the squared term: Divide each side by '150'. -66207.92167 + -332.3722x + x2 = 0 Move the constant term to the right: Add '66207.92167' to each side of the equation. -66207.92167 + -332.3722x + 66207.92167 + x2 = 0 + 66207.92167 Reorder the terms: -66207.92167 + 66207.92167 + -332.3722x + x2 = 0 + 66207.92167 Combine like terms: -66207.92167 + 66207.92167 = 0.00000 0.00000 + -332.3722x + x2 = 0 + 66207.92167 -332.3722x + x2 = 0 + 66207.92167 Combine like terms: 0 + 66207.92167 = 66207.92167 -332.3722x + x2 = 66207.92167 The x term is -332.3722x. Take half its coefficient (-166.1861). Square it (27617.81983) and add it to both sides. Add '27617.81983' to each side of the equation. -332.3722x + 27617.81983 + x2 = 66207.92167 + 27617.81983 Reorder the terms: 27617.81983 + -332.3722x + x2 = 66207.92167 + 27617.81983 Combine like terms: 66207.92167 + 27617.81983 = 93825.7415 27617.81983 + -332.3722x + x2 = 93825.7415 Factor a perfect square on the left side: (x + -166.1861)(x + -166.1861) = 93825.7415 Calculate the square root of the right side: 306.309878228 Break this problem into two subproblems by setting (x + -166.1861) equal to 306.309878228 and -306.309878228.Subproblem 1
x + -166.1861 = 306.309878228 Simplifying x + -166.1861 = 306.309878228 Reorder the terms: -166.1861 + x = 306.309878228 Solving -166.1861 + x = 306.309878228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.1861' to each side of the equation. -166.1861 + 166.1861 + x = 306.309878228 + 166.1861 Combine like terms: -166.1861 + 166.1861 = 0.0000 0.0000 + x = 306.309878228 + 166.1861 x = 306.309878228 + 166.1861 Combine like terms: 306.309878228 + 166.1861 = 472.495978228 x = 472.495978228 Simplifying x = 472.495978228Subproblem 2
x + -166.1861 = -306.309878228 Simplifying x + -166.1861 = -306.309878228 Reorder the terms: -166.1861 + x = -306.309878228 Solving -166.1861 + x = -306.309878228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.1861' to each side of the equation. -166.1861 + 166.1861 + x = -306.309878228 + 166.1861 Combine like terms: -166.1861 + 166.1861 = 0.0000 0.0000 + x = -306.309878228 + 166.1861 x = -306.309878228 + 166.1861 Combine like terms: -306.309878228 + 166.1861 = -140.123778228 x = -140.123778228 Simplifying x = -140.123778228Solution
The solution to the problem is based on the solutions from the subproblems. x = {472.495978228, -140.123778228}
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