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Simplifying 17x2 + 23x + -160 = 0 Reorder the terms: -160 + 23x + 17x2 = 0 Solving -160 + 23x + 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'. -9.411764706 + 1.352941176x + x2 = 0 Move the constant term to the right: Add '9.411764706' to each side of the equation. -9.411764706 + 1.352941176x + 9.411764706 + x2 = 0 + 9.411764706 Reorder the terms: -9.411764706 + 9.411764706 + 1.352941176x + x2 = 0 + 9.411764706 Combine like terms: -9.411764706 + 9.411764706 = 0.000000000 0.000000000 + 1.352941176x + x2 = 0 + 9.411764706 1.352941176x + x2 = 0 + 9.411764706 Combine like terms: 0 + 9.411764706 = 9.411764706 1.352941176x + x2 = 9.411764706 The x term is 1.352941176x. Take half its coefficient (0.676470588). Square it (0.4576124564) and add it to both sides. Add '0.4576124564' to each side of the equation. 1.352941176x + 0.4576124564 + x2 = 9.411764706 + 0.4576124564 Reorder the terms: 0.4576124564 + 1.352941176x + x2 = 9.411764706 + 0.4576124564 Combine like terms: 9.411764706 + 0.4576124564 = 9.8693771624 0.4576124564 + 1.352941176x + x2 = 9.8693771624 Factor a perfect square on the left side: (x + 0.676470588)(x + 0.676470588) = 9.8693771624 Calculate the square root of the right side: 3.141556487 Break this problem into two subproblems by setting (x + 0.676470588) equal to 3.141556487 and -3.141556487.Subproblem 1
x + 0.676470588 = 3.141556487 Simplifying x + 0.676470588 = 3.141556487 Reorder the terms: 0.676470588 + x = 3.141556487 Solving 0.676470588 + x = 3.141556487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + x = 3.141556487 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + x = 3.141556487 + -0.676470588 x = 3.141556487 + -0.676470588 Combine like terms: 3.141556487 + -0.676470588 = 2.465085899 x = 2.465085899 Simplifying x = 2.465085899Subproblem 2
x + 0.676470588 = -3.141556487 Simplifying x + 0.676470588 = -3.141556487 Reorder the terms: 0.676470588 + x = -3.141556487 Solving 0.676470588 + x = -3.141556487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + x = -3.141556487 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + x = -3.141556487 + -0.676470588 x = -3.141556487 + -0.676470588 Combine like terms: -3.141556487 + -0.676470588 = -3.818027075 x = -3.818027075 Simplifying x = -3.818027075Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.465085899, -3.818027075}
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