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Simplifying 11x2 + -32x + 3 = 0 Reorder the terms: 3 + -32x + 11x2 = 0 Solving 3 + -32x + 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 + -2.909090909x + x2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + -2.909090909x + -0.2727272727 + x2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + -2.909090909x + x2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + -2.909090909x + x2 = 0 + -0.2727272727 -2.909090909x + x2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 -2.909090909x + x2 = -0.2727272727 The x term is -2.909090909x. Take half its coefficient (-1.454545455). Square it (2.115702481) and add it to both sides. Add '2.115702481' to each side of the equation. -2.909090909x + 2.115702481 + x2 = -0.2727272727 + 2.115702481 Reorder the terms: 2.115702481 + -2.909090909x + x2 = -0.2727272727 + 2.115702481 Combine like terms: -0.2727272727 + 2.115702481 = 1.8429752083 2.115702481 + -2.909090909x + x2 = 1.8429752083 Factor a perfect square on the left side: (x + -1.454545455)(x + -1.454545455) = 1.8429752083 Calculate the square root of the right side: 1.35756223 Break this problem into two subproblems by setting (x + -1.454545455) equal to 1.35756223 and -1.35756223.Subproblem 1
x + -1.454545455 = 1.35756223 Simplifying x + -1.454545455 = 1.35756223 Reorder the terms: -1.454545455 + x = 1.35756223 Solving -1.454545455 + x = 1.35756223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + x = 1.35756223 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + x = 1.35756223 + 1.454545455 x = 1.35756223 + 1.454545455 Combine like terms: 1.35756223 + 1.454545455 = 2.812107685 x = 2.812107685 Simplifying x = 2.812107685Subproblem 2
x + -1.454545455 = -1.35756223 Simplifying x + -1.454545455 = -1.35756223 Reorder the terms: -1.454545455 + x = -1.35756223 Solving -1.454545455 + x = -1.35756223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + x = -1.35756223 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + x = -1.35756223 + 1.454545455 x = -1.35756223 + 1.454545455 Combine like terms: -1.35756223 + 1.454545455 = 0.096983225 x = 0.096983225 Simplifying x = 0.096983225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.812107685, 0.096983225}
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