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Simplifying 100x + -11x2 + -6 = 0 Reorder the terms: -6 + 100x + -11x2 = 0 Solving -6 + 100x + -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'. 0.5454545455 + -9.090909091x + x2 = 0 Move the constant term to the right: Add '-0.5454545455' to each side of the equation. 0.5454545455 + -9.090909091x + -0.5454545455 + x2 = 0 + -0.5454545455 Reorder the terms: 0.5454545455 + -0.5454545455 + -9.090909091x + x2 = 0 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + -9.090909091x + x2 = 0 + -0.5454545455 -9.090909091x + x2 = 0 + -0.5454545455 Combine like terms: 0 + -0.5454545455 = -0.5454545455 -9.090909091x + x2 = -0.5454545455 The x term is -9.090909091x. Take half its coefficient (-4.545454546). Square it (20.66115703) and add it to both sides. Add '20.66115703' to each side of the equation. -9.090909091x + 20.66115703 + x2 = -0.5454545455 + 20.66115703 Reorder the terms: 20.66115703 + -9.090909091x + x2 = -0.5454545455 + 20.66115703 Combine like terms: -0.5454545455 + 20.66115703 = 20.1157024845 20.66115703 + -9.090909091x + x2 = 20.1157024845 Factor a perfect square on the left side: (x + -4.545454546)(x + -4.545454546) = 20.1157024845 Calculate the square root of the right side: 4.485053231 Break this problem into two subproblems by setting (x + -4.545454546) equal to 4.485053231 and -4.485053231.Subproblem 1
x + -4.545454546 = 4.485053231 Simplifying x + -4.545454546 = 4.485053231 Reorder the terms: -4.545454546 + x = 4.485053231 Solving -4.545454546 + x = 4.485053231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.545454546' to each side of the equation. -4.545454546 + 4.545454546 + x = 4.485053231 + 4.545454546 Combine like terms: -4.545454546 + 4.545454546 = 0.000000000 0.000000000 + x = 4.485053231 + 4.545454546 x = 4.485053231 + 4.545454546 Combine like terms: 4.485053231 + 4.545454546 = 9.030507777 x = 9.030507777 Simplifying x = 9.030507777Subproblem 2
x + -4.545454546 = -4.485053231 Simplifying x + -4.545454546 = -4.485053231 Reorder the terms: -4.545454546 + x = -4.485053231 Solving -4.545454546 + x = -4.485053231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.545454546' to each side of the equation. -4.545454546 + 4.545454546 + x = -4.485053231 + 4.545454546 Combine like terms: -4.545454546 + 4.545454546 = 0.000000000 0.000000000 + x = -4.485053231 + 4.545454546 x = -4.485053231 + 4.545454546 Combine like terms: -4.485053231 + 4.545454546 = 0.060401315 x = 0.060401315 Simplifying x = 0.060401315Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.030507777, 0.060401315}
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