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Simplifying 3x2 + -3x + -64 = 0 Reorder the terms: -64 + -3x + 3x2 = 0 Solving -64 + -3x + 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 + -1x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + -1x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + -1x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + -1x + x2 = 0 + 21.33333333 -1x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 -1x + x2 = 21.33333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 21.33333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 21.33333333 + 0.25 Combine like terms: 21.33333333 + 0.25 = 21.58333333 0.25 + -1x + x2 = 21.58333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 21.58333333 Calculate the square root of the right side: 4.645786621 Break this problem into two subproblems by setting (x + -0.5) equal to 4.645786621 and -4.645786621.Subproblem 1
x + -0.5 = 4.645786621 Simplifying x + -0.5 = 4.645786621 Reorder the terms: -0.5 + x = 4.645786621 Solving -0.5 + x = 4.645786621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.645786621 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.645786621 + 0.5 x = 4.645786621 + 0.5 Combine like terms: 4.645786621 + 0.5 = 5.145786621 x = 5.145786621 Simplifying x = 5.145786621Subproblem 2
x + -0.5 = -4.645786621 Simplifying x + -0.5 = -4.645786621 Reorder the terms: -0.5 + x = -4.645786621 Solving -0.5 + x = -4.645786621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.645786621 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.645786621 + 0.5 x = -4.645786621 + 0.5 Combine like terms: -4.645786621 + 0.5 = -4.145786621 x = -4.145786621 Simplifying x = -4.145786621Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.145786621, -4.145786621}
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