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Simplifying 9x2 + -54x + 20 = 0 Reorder the terms: 20 + -54x + 9x2 = 0 Solving 20 + -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'. 2.222222222 + -6x + x2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + -6x + -2.222222222 + x2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + -6x + x2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + -6x + x2 = 0 + -2.222222222 -6x + x2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 -6x + x2 = -2.222222222 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 = -2.222222222 + 9 Reorder the terms: 9 + -6x + x2 = -2.222222222 + 9 Combine like terms: -2.222222222 + 9 = 6.777777778 9 + -6x + x2 = 6.777777778 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.777777778 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + -3) equal to 2.603416559 and -2.603416559.Subproblem 1
x + -3 = 2.603416559 Simplifying x + -3 = 2.603416559 Reorder the terms: -3 + x = 2.603416559 Solving -3 + x = 2.603416559 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 = 2.603416559 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.603416559 + 3 x = 2.603416559 + 3 Combine like terms: 2.603416559 + 3 = 5.603416559 x = 5.603416559 Simplifying x = 5.603416559Subproblem 2
x + -3 = -2.603416559 Simplifying x + -3 = -2.603416559 Reorder the terms: -3 + x = -2.603416559 Solving -3 + x = -2.603416559 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 = -2.603416559 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.603416559 + 3 x = -2.603416559 + 3 Combine like terms: -2.603416559 + 3 = 0.396583441 x = 0.396583441 Simplifying x = 0.396583441Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.603416559, 0.396583441}
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