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Simplifying 9x2 + -41x + -92 = 0 Reorder the terms: -92 + -41x + 9x2 = 0 Solving -92 + -41x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -10.22222222 + -4.555555556x + x2 = 0 Move the constant term to the right: Add '10.22222222' to each side of the equation. -10.22222222 + -4.555555556x + 10.22222222 + x2 = 0 + 10.22222222 Reorder the terms: -10.22222222 + 10.22222222 + -4.555555556x + x2 = 0 + 10.22222222 Combine like terms: -10.22222222 + 10.22222222 = 0.00000000 0.00000000 + -4.555555556x + x2 = 0 + 10.22222222 -4.555555556x + x2 = 0 + 10.22222222 Combine like terms: 0 + 10.22222222 = 10.22222222 -4.555555556x + x2 = 10.22222222 The x term is -4.555555556x. Take half its coefficient (-2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. -4.555555556x + 5.188271606 + x2 = 10.22222222 + 5.188271606 Reorder the terms: 5.188271606 + -4.555555556x + x2 = 10.22222222 + 5.188271606 Combine like terms: 10.22222222 + 5.188271606 = 15.410493826 5.188271606 + -4.555555556x + x2 = 15.410493826 Factor a perfect square on the left side: (x + -2.277777778)(x + -2.277777778) = 15.410493826 Calculate the square root of the right side: 3.925620184 Break this problem into two subproblems by setting (x + -2.277777778) equal to 3.925620184 and -3.925620184.Subproblem 1
x + -2.277777778 = 3.925620184 Simplifying x + -2.277777778 = 3.925620184 Reorder the terms: -2.277777778 + x = 3.925620184 Solving -2.277777778 + x = 3.925620184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = 3.925620184 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = 3.925620184 + 2.277777778 x = 3.925620184 + 2.277777778 Combine like terms: 3.925620184 + 2.277777778 = 6.203397962 x = 6.203397962 Simplifying x = 6.203397962Subproblem 2
x + -2.277777778 = -3.925620184 Simplifying x + -2.277777778 = -3.925620184 Reorder the terms: -2.277777778 + x = -3.925620184 Solving -2.277777778 + x = -3.925620184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = -3.925620184 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = -3.925620184 + 2.277777778 x = -3.925620184 + 2.277777778 Combine like terms: -3.925620184 + 2.277777778 = -1.647842406 x = -1.647842406 Simplifying x = -1.647842406Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.203397962, -1.647842406}
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