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Simplifying 9x2 + -82x + 81 = 0 Reorder the terms: 81 + -82x + 9x2 = 0 Solving 81 + -82x + 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'. 9 + -9.111111111x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9.111111111x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9.111111111x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9.111111111x + x2 = 0 + -9 -9.111111111x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9.111111111x + x2 = -9 The x term is -9.111111111x. Take half its coefficient (-4.555555556). Square it (20.75308642) and add it to both sides. Add '20.75308642' to each side of the equation. -9.111111111x + 20.75308642 + x2 = -9 + 20.75308642 Reorder the terms: 20.75308642 + -9.111111111x + x2 = -9 + 20.75308642 Combine like terms: -9 + 20.75308642 = 11.75308642 20.75308642 + -9.111111111x + x2 = 11.75308642 Factor a perfect square on the left side: (x + -4.555555556)(x + -4.555555556) = 11.75308642 Calculate the square root of the right side: 3.428277471 Break this problem into two subproblems by setting (x + -4.555555556) equal to 3.428277471 and -3.428277471.Subproblem 1
x + -4.555555556 = 3.428277471 Simplifying x + -4.555555556 = 3.428277471 Reorder the terms: -4.555555556 + x = 3.428277471 Solving -4.555555556 + x = 3.428277471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.555555556' to each side of the equation. -4.555555556 + 4.555555556 + x = 3.428277471 + 4.555555556 Combine like terms: -4.555555556 + 4.555555556 = 0.000000000 0.000000000 + x = 3.428277471 + 4.555555556 x = 3.428277471 + 4.555555556 Combine like terms: 3.428277471 + 4.555555556 = 7.983833027 x = 7.983833027 Simplifying x = 7.983833027Subproblem 2
x + -4.555555556 = -3.428277471 Simplifying x + -4.555555556 = -3.428277471 Reorder the terms: -4.555555556 + x = -3.428277471 Solving -4.555555556 + x = -3.428277471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.555555556' to each side of the equation. -4.555555556 + 4.555555556 + x = -3.428277471 + 4.555555556 Combine like terms: -4.555555556 + 4.555555556 = 0.000000000 0.000000000 + x = -3.428277471 + 4.555555556 x = -3.428277471 + 4.555555556 Combine like terms: -3.428277471 + 4.555555556 = 1.127278085 x = 1.127278085 Simplifying x = 1.127278085Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.983833027, 1.127278085}
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