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Simplifying 0.29x2 + -16.5x + -1761 = 0 Reorder the terms: -1761 + -16.5x + 0.29x2 = 0 Solving -1761 + -16.5x + 0.29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. -6072.413793 + -56.89655172x + x2 = 0 Move the constant term to the right: Add '6072.413793' to each side of the equation. -6072.413793 + -56.89655172x + 6072.413793 + x2 = 0 + 6072.413793 Reorder the terms: -6072.413793 + 6072.413793 + -56.89655172x + x2 = 0 + 6072.413793 Combine like terms: -6072.413793 + 6072.413793 = 0.000000 0.000000 + -56.89655172x + x2 = 0 + 6072.413793 -56.89655172x + x2 = 0 + 6072.413793 Combine like terms: 0 + 6072.413793 = 6072.413793 -56.89655172x + x2 = 6072.413793 The x term is -56.89655172x. Take half its coefficient (-28.44827586). Square it (809.3043994) and add it to both sides. Add '809.3043994' to each side of the equation. -56.89655172x + 809.3043994 + x2 = 6072.413793 + 809.3043994 Reorder the terms: 809.3043994 + -56.89655172x + x2 = 6072.413793 + 809.3043994 Combine like terms: 6072.413793 + 809.3043994 = 6881.7181924 809.3043994 + -56.89655172x + x2 = 6881.7181924 Factor a perfect square on the left side: (x + -28.44827586)(x + -28.44827586) = 6881.7181924 Calculate the square root of the right side: 82.956122091 Break this problem into two subproblems by setting (x + -28.44827586) equal to 82.956122091 and -82.956122091.Subproblem 1
x + -28.44827586 = 82.956122091 Simplifying x + -28.44827586 = 82.956122091 Reorder the terms: -28.44827586 + x = 82.956122091 Solving -28.44827586 + x = 82.956122091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.44827586' to each side of the equation. -28.44827586 + 28.44827586 + x = 82.956122091 + 28.44827586 Combine like terms: -28.44827586 + 28.44827586 = 0.00000000 0.00000000 + x = 82.956122091 + 28.44827586 x = 82.956122091 + 28.44827586 Combine like terms: 82.956122091 + 28.44827586 = 111.404397951 x = 111.404397951 Simplifying x = 111.404397951Subproblem 2
x + -28.44827586 = -82.956122091 Simplifying x + -28.44827586 = -82.956122091 Reorder the terms: -28.44827586 + x = -82.956122091 Solving -28.44827586 + x = -82.956122091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.44827586' to each side of the equation. -28.44827586 + 28.44827586 + x = -82.956122091 + 28.44827586 Combine like terms: -28.44827586 + 28.44827586 = 0.00000000 0.00000000 + x = -82.956122091 + 28.44827586 x = -82.956122091 + 28.44827586 Combine like terms: -82.956122091 + 28.44827586 = -54.507846231 x = -54.507846231 Simplifying x = -54.507846231Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.404397951, -54.507846231}
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