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Simplifying 9x2 + -54x + -1 = 0 Reorder the terms: -1 + -54x + 9x2 = 0 Solving -1 + -54x + 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'. -0.1111111111 + -6x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -6x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -6x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + 0.1111111111 -6x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -6x + x2 = 0.1111111111 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.1111111111 + 9 Reorder the terms: 9 + -6x + x2 = 0.1111111111 + 9 Combine like terms: 0.1111111111 + 9 = 9.1111111111 9 + -6x + x2 = 9.1111111111 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.1111111111 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + -3) equal to 3.018461713 and -3.018461713.Subproblem 1
x + -3 = 3.018461713 Simplifying x + -3 = 3.018461713 Reorder the terms: -3 + x = 3.018461713 Solving -3 + x = 3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.018461713 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.018461713 + 3 x = 3.018461713 + 3 Combine like terms: 3.018461713 + 3 = 6.018461713 x = 6.018461713 Simplifying x = 6.018461713Subproblem 2
x + -3 = -3.018461713 Simplifying x + -3 = -3.018461713 Reorder the terms: -3 + x = -3.018461713 Solving -3 + x = -3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.018461713 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.018461713 + 3 x = -3.018461713 + 3 Combine like terms: -3.018461713 + 3 = -0.018461713 x = -0.018461713 Simplifying x = -0.018461713Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.018461713, -0.018461713}
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