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Simplifying 17x2 + -44x + -50 = 0 Reorder the terms: -50 + -44x + 17x2 = 0 Solving -50 + -44x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -2.941176471 + -2.588235294x + x2 = 0 Move the constant term to the right: Add '2.941176471' to each side of the equation. -2.941176471 + -2.588235294x + 2.941176471 + x2 = 0 + 2.941176471 Reorder the terms: -2.941176471 + 2.941176471 + -2.588235294x + x2 = 0 + 2.941176471 Combine like terms: -2.941176471 + 2.941176471 = 0.000000000 0.000000000 + -2.588235294x + x2 = 0 + 2.941176471 -2.588235294x + x2 = 0 + 2.941176471 Combine like terms: 0 + 2.941176471 = 2.941176471 -2.588235294x + x2 = 2.941176471 The x term is -2.588235294x. Take half its coefficient (-1.294117647). Square it (1.674740484) and add it to both sides. Add '1.674740484' to each side of the equation. -2.588235294x + 1.674740484 + x2 = 2.941176471 + 1.674740484 Reorder the terms: 1.674740484 + -2.588235294x + x2 = 2.941176471 + 1.674740484 Combine like terms: 2.941176471 + 1.674740484 = 4.615916955 1.674740484 + -2.588235294x + x2 = 4.615916955 Factor a perfect square on the left side: (x + -1.294117647)(x + -1.294117647) = 4.615916955 Calculate the square root of the right side: 2.148468514 Break this problem into two subproblems by setting (x + -1.294117647) equal to 2.148468514 and -2.148468514.Subproblem 1
x + -1.294117647 = 2.148468514 Simplifying x + -1.294117647 = 2.148468514 Reorder the terms: -1.294117647 + x = 2.148468514 Solving -1.294117647 + x = 2.148468514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.294117647' to each side of the equation. -1.294117647 + 1.294117647 + x = 2.148468514 + 1.294117647 Combine like terms: -1.294117647 + 1.294117647 = 0.000000000 0.000000000 + x = 2.148468514 + 1.294117647 x = 2.148468514 + 1.294117647 Combine like terms: 2.148468514 + 1.294117647 = 3.442586161 x = 3.442586161 Simplifying x = 3.442586161Subproblem 2
x + -1.294117647 = -2.148468514 Simplifying x + -1.294117647 = -2.148468514 Reorder the terms: -1.294117647 + x = -2.148468514 Solving -1.294117647 + x = -2.148468514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.294117647' to each side of the equation. -1.294117647 + 1.294117647 + x = -2.148468514 + 1.294117647 Combine like terms: -1.294117647 + 1.294117647 = 0.000000000 0.000000000 + x = -2.148468514 + 1.294117647 x = -2.148468514 + 1.294117647 Combine like terms: -2.148468514 + 1.294117647 = -0.854350867 x = -0.854350867 Simplifying x = -0.854350867Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.442586161, -0.854350867}
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