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Simplifying 3x2 + -8x + -18 = 0 Reorder the terms: -18 + -8x + 3x2 = 0 Solving -18 + -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'. -6 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.666666667x + x2 = 0 + 6 -2.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.666666667x + x2 = 6 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 = 6 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 6 + 1.777777780 Combine like terms: 6 + 1.777777780 = 7.77777778 1.777777780 + -2.666666667x + x2 = 7.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 7.77777778 Calculate the square root of the right side: 2.788866756 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.788866756 and -2.788866756.Subproblem 1
x + -1.333333334 = 2.788866756 Simplifying x + -1.333333334 = 2.788866756 Reorder the terms: -1.333333334 + x = 2.788866756 Solving -1.333333334 + x = 2.788866756 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 = 2.788866756 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.788866756 + 1.333333334 x = 2.788866756 + 1.333333334 Combine like terms: 2.788866756 + 1.333333334 = 4.12220009 x = 4.12220009 Simplifying x = 4.12220009Subproblem 2
x + -1.333333334 = -2.788866756 Simplifying x + -1.333333334 = -2.788866756 Reorder the terms: -1.333333334 + x = -2.788866756 Solving -1.333333334 + x = -2.788866756 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 = -2.788866756 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.788866756 + 1.333333334 x = -2.788866756 + 1.333333334 Combine like terms: -2.788866756 + 1.333333334 = -1.455533422 x = -1.455533422 Simplifying x = -1.455533422Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.12220009, -1.455533422}
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