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Simplifying 11x2 + -16x + 3 = 0 Reorder the terms: 3 + -16x + 11x2 = 0 Solving 3 + -16x + 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 + -1.454545455x + x2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + -1.454545455x + -0.2727272727 + x2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + -1.454545455x + x2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + -1.454545455x + x2 = 0 + -0.2727272727 -1.454545455x + x2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 -1.454545455x + x2 = -0.2727272727 The x term is -1.454545455x. Take half its coefficient (-0.7272727275). Square it (0.5289256202) and add it to both sides. Add '0.5289256202' to each side of the equation. -1.454545455x + 0.5289256202 + x2 = -0.2727272727 + 0.5289256202 Reorder the terms: 0.5289256202 + -1.454545455x + x2 = -0.2727272727 + 0.5289256202 Combine like terms: -0.2727272727 + 0.5289256202 = 0.2561983475 0.5289256202 + -1.454545455x + x2 = 0.2561983475 Factor a perfect square on the left side: (x + -0.7272727275)(x + -0.7272727275) = 0.2561983475 Calculate the square root of the right side: 0.506160397 Break this problem into two subproblems by setting (x + -0.7272727275) equal to 0.506160397 and -0.506160397.Subproblem 1
x + -0.7272727275 = 0.506160397 Simplifying x + -0.7272727275 = 0.506160397 Reorder the terms: -0.7272727275 + x = 0.506160397 Solving -0.7272727275 + x = 0.506160397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = 0.506160397 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = 0.506160397 + 0.7272727275 x = 0.506160397 + 0.7272727275 Combine like terms: 0.506160397 + 0.7272727275 = 1.2334331245 x = 1.2334331245 Simplifying x = 1.2334331245Subproblem 2
x + -0.7272727275 = -0.506160397 Simplifying x + -0.7272727275 = -0.506160397 Reorder the terms: -0.7272727275 + x = -0.506160397 Solving -0.7272727275 + x = -0.506160397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = -0.506160397 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = -0.506160397 + 0.7272727275 x = -0.506160397 + 0.7272727275 Combine like terms: -0.506160397 + 0.7272727275 = 0.2211123305 x = 0.2211123305 Simplifying x = 0.2211123305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2334331245, 0.2211123305}
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