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Simplifying 3x2 + -8x + -81 = 0 Reorder the terms: -81 + -8x + 3x2 = 0 Solving -81 + -8x + 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'. -27 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -2.666666667x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -2.666666667x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2.666666667x + x2 = 0 + 27 -2.666666667x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2.666666667x + x2 = 27 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 27 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 27 + 1.777777780 Combine like terms: 27 + 1.777777780 = 28.77777778 1.777777780 + -2.666666667x + x2 = 28.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 28.77777778 Calculate the square root of the right side: 5.364492313 Break this problem into two subproblems by setting (x + -1.333333334) equal to 5.364492313 and -5.364492313.Subproblem 1
x + -1.333333334 = 5.364492313 Simplifying x + -1.333333334 = 5.364492313 Reorder the terms: -1.333333334 + x = 5.364492313 Solving -1.333333334 + x = 5.364492313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 5.364492313 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 5.364492313 + 1.333333334 x = 5.364492313 + 1.333333334 Combine like terms: 5.364492313 + 1.333333334 = 6.697825647 x = 6.697825647 Simplifying x = 6.697825647Subproblem 2
x + -1.333333334 = -5.364492313 Simplifying x + -1.333333334 = -5.364492313 Reorder the terms: -1.333333334 + x = -5.364492313 Solving -1.333333334 + x = -5.364492313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -5.364492313 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -5.364492313 + 1.333333334 x = -5.364492313 + 1.333333334 Combine like terms: -5.364492313 + 1.333333334 = -4.031158979 x = -4.031158979 Simplifying x = -4.031158979Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.697825647, -4.031158979}
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