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Simplifying 11x2 + -17x + -3 = 0 Reorder the terms: -3 + -17x + 11x2 = 0 Solving -3 + -17x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -1.545454545x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -1.545454545x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -1.545454545x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -1.545454545x + x2 = 0 + 0.2727272727 -1.545454545x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -1.545454545x + x2 = 0.2727272727 The x term is -1.545454545x. Take half its coefficient (-0.7727272725). Square it (0.5971074377) and add it to both sides. Add '0.5971074377' to each side of the equation. -1.545454545x + 0.5971074377 + x2 = 0.2727272727 + 0.5971074377 Reorder the terms: 0.5971074377 + -1.545454545x + x2 = 0.2727272727 + 0.5971074377 Combine like terms: 0.2727272727 + 0.5971074377 = 0.8698347104 0.5971074377 + -1.545454545x + x2 = 0.8698347104 Factor a perfect square on the left side: (x + -0.7727272725)(x + -0.7727272725) = 0.8698347104 Calculate the square root of the right side: 0.932649297 Break this problem into two subproblems by setting (x + -0.7727272725) equal to 0.932649297 and -0.932649297.Subproblem 1
x + -0.7727272725 = 0.932649297 Simplifying x + -0.7727272725 = 0.932649297 Reorder the terms: -0.7727272725 + x = 0.932649297 Solving -0.7727272725 + x = 0.932649297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7727272725' to each side of the equation. -0.7727272725 + 0.7727272725 + x = 0.932649297 + 0.7727272725 Combine like terms: -0.7727272725 + 0.7727272725 = 0.0000000000 0.0000000000 + x = 0.932649297 + 0.7727272725 x = 0.932649297 + 0.7727272725 Combine like terms: 0.932649297 + 0.7727272725 = 1.7053765695 x = 1.7053765695 Simplifying x = 1.7053765695Subproblem 2
x + -0.7727272725 = -0.932649297 Simplifying x + -0.7727272725 = -0.932649297 Reorder the terms: -0.7727272725 + x = -0.932649297 Solving -0.7727272725 + x = -0.932649297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7727272725' to each side of the equation. -0.7727272725 + 0.7727272725 + x = -0.932649297 + 0.7727272725 Combine like terms: -0.7727272725 + 0.7727272725 = 0.0000000000 0.0000000000 + x = -0.932649297 + 0.7727272725 x = -0.932649297 + 0.7727272725 Combine like terms: -0.932649297 + 0.7727272725 = -0.1599220245 x = -0.1599220245 Simplifying x = -0.1599220245Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7053765695, -0.1599220245}
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