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Simplifying 9x2 + -27x + -35 = 0 Reorder the terms: -35 + -27x + 9x2 = 0 Solving -35 + -27x + 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'. -3.888888889 + -3x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -3x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -3x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -3x + x2 = 0 + 3.888888889 -3x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -3x + x2 = 3.888888889 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 3.888888889 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.888888889 + 2.25 Combine like terms: 3.888888889 + 2.25 = 6.138888889 2.25 + -3x + x2 = 6.138888889 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.138888889 Calculate the square root of the right side: 2.477678125 Break this problem into two subproblems by setting (x + -1.5) equal to 2.477678125 and -2.477678125.Subproblem 1
x + -1.5 = 2.477678125 Simplifying x + -1.5 = 2.477678125 Reorder the terms: -1.5 + x = 2.477678125 Solving -1.5 + x = 2.477678125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.477678125 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.477678125 + 1.5 x = 2.477678125 + 1.5 Combine like terms: 2.477678125 + 1.5 = 3.977678125 x = 3.977678125 Simplifying x = 3.977678125Subproblem 2
x + -1.5 = -2.477678125 Simplifying x + -1.5 = -2.477678125 Reorder the terms: -1.5 + x = -2.477678125 Solving -1.5 + x = -2.477678125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.477678125 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.477678125 + 1.5 x = -2.477678125 + 1.5 Combine like terms: -2.477678125 + 1.5 = -0.977678125 x = -0.977678125 Simplifying x = -0.977678125Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.977678125, -0.977678125}
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