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Simplifying 3x2 + -18x + -64 = 0 Reorder the terms: -64 + -18x + 3x2 = 0 Solving -64 + -18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + -6x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + -6x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + -6x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + -6x + x2 = 0 + 21.33333333 -6x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 -6x + x2 = 21.33333333 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 = 21.33333333 + 9 Reorder the terms: 9 + -6x + x2 = 21.33333333 + 9 Combine like terms: 21.33333333 + 9 = 30.33333333 9 + -6x + x2 = 30.33333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 30.33333333 Calculate the square root of the right side: 5.507570547 Break this problem into two subproblems by setting (x + -3) equal to 5.507570547 and -5.507570547.Subproblem 1
x + -3 = 5.507570547 Simplifying x + -3 = 5.507570547 Reorder the terms: -3 + x = 5.507570547 Solving -3 + x = 5.507570547 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 = 5.507570547 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.507570547 + 3 x = 5.507570547 + 3 Combine like terms: 5.507570547 + 3 = 8.507570547 x = 8.507570547 Simplifying x = 8.507570547Subproblem 2
x + -3 = -5.507570547 Simplifying x + -3 = -5.507570547 Reorder the terms: -3 + x = -5.507570547 Solving -3 + x = -5.507570547 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 = -5.507570547 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.507570547 + 3 x = -5.507570547 + 3 Combine like terms: -5.507570547 + 3 = -2.507570547 x = -2.507570547 Simplifying x = -2.507570547Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.507570547, -2.507570547}
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