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Simplifying 5x + 6 + -11x2 + 90.64 = 0 Reorder the terms: 6 + 90.64 + 5x + -11x2 = 0 Combine like terms: 6 + 90.64 = 96.64 96.64 + 5x + -11x2 = 0 Solving 96.64 + 5x + -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'. -8.785454545 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '8.785454545' to each side of the equation. -8.785454545 + -0.4545454545x + 8.785454545 + x2 = 0 + 8.785454545 Reorder the terms: -8.785454545 + 8.785454545 + -0.4545454545x + x2 = 0 + 8.785454545 Combine like terms: -8.785454545 + 8.785454545 = 0.000000000 0.000000000 + -0.4545454545x + x2 = 0 + 8.785454545 -0.4545454545x + x2 = 0 + 8.785454545 Combine like terms: 0 + 8.785454545 = 8.785454545 -0.4545454545x + x2 = 8.785454545 The x term is -0.4545454545x. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545x + 0.05165289257 + x2 = 8.785454545 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 8.785454545 + 0.05165289257 Combine like terms: 8.785454545 + 0.05165289257 = 8.83710743757 0.05165289257 + -0.4545454545x + x2 = 8.83710743757 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 8.83710743757 Calculate the square root of the right side: 2.972727273 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 2.972727273 and -2.972727273.Subproblem 1
x + -0.2272727273 = 2.972727273 Simplifying x + -0.2272727273 = 2.972727273 Reorder the terms: -0.2272727273 + x = 2.972727273 Solving -0.2272727273 + x = 2.972727273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = 2.972727273 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 2.972727273 + 0.2272727273 x = 2.972727273 + 0.2272727273 Combine like terms: 2.972727273 + 0.2272727273 = 3.2000000003 x = 3.2000000003 Simplifying x = 3.2000000003Subproblem 2
x + -0.2272727273 = -2.972727273 Simplifying x + -0.2272727273 = -2.972727273 Reorder the terms: -0.2272727273 + x = -2.972727273 Solving -0.2272727273 + x = -2.972727273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = -2.972727273 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -2.972727273 + 0.2272727273 x = -2.972727273 + 0.2272727273 Combine like terms: -2.972727273 + 0.2272727273 = -2.7454545457 x = -2.7454545457 Simplifying x = -2.7454545457Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2000000003, -2.7454545457}
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