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Simplifying 3x2 + -3x + -44 = 0 Reorder the terms: -44 + -3x + 3x2 = 0 Solving -44 + -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'. -14.66666667 + -1x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -1x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -1x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -1x + x2 = 0 + 14.66666667 -1x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -1x + x2 = 14.66666667 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 = 14.66666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 14.66666667 + 0.25 Combine like terms: 14.66666667 + 0.25 = 14.91666667 0.25 + -1x + x2 = 14.91666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 14.91666667 Calculate the square root of the right side: 3.862210076 Break this problem into two subproblems by setting (x + -0.5) equal to 3.862210076 and -3.862210076.Subproblem 1
x + -0.5 = 3.862210076 Simplifying x + -0.5 = 3.862210076 Reorder the terms: -0.5 + x = 3.862210076 Solving -0.5 + x = 3.862210076 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 = 3.862210076 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.862210076 + 0.5 x = 3.862210076 + 0.5 Combine like terms: 3.862210076 + 0.5 = 4.362210076 x = 4.362210076 Simplifying x = 4.362210076Subproblem 2
x + -0.5 = -3.862210076 Simplifying x + -0.5 = -3.862210076 Reorder the terms: -0.5 + x = -3.862210076 Solving -0.5 + x = -3.862210076 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 = -3.862210076 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.862210076 + 0.5 x = -3.862210076 + 0.5 Combine like terms: -3.862210076 + 0.5 = -3.362210076 x = -3.362210076 Simplifying x = -3.362210076Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.362210076, -3.362210076}
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