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Simplifying 3x2 + 8x + -138 = 0 Reorder the terms: -138 + 8x + 3x2 = 0 Solving -138 + 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'. -46 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + 2.666666667x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 2.666666667x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 2.666666667x + x2 = 0 + 46 2.666666667x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 2.666666667x + x2 = 46 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 = 46 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 46 + 1.777777780 Combine like terms: 46 + 1.777777780 = 47.77777778 1.777777780 + 2.666666667x + x2 = 47.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 47.77777778 Calculate the square root of the right side: 6.912147118 Break this problem into two subproblems by setting (x + 1.333333334) equal to 6.912147118 and -6.912147118.Subproblem 1
x + 1.333333334 = 6.912147118 Simplifying x + 1.333333334 = 6.912147118 Reorder the terms: 1.333333334 + x = 6.912147118 Solving 1.333333334 + x = 6.912147118 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 = 6.912147118 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 6.912147118 + -1.333333334 x = 6.912147118 + -1.333333334 Combine like terms: 6.912147118 + -1.333333334 = 5.578813784 x = 5.578813784 Simplifying x = 5.578813784Subproblem 2
x + 1.333333334 = -6.912147118 Simplifying x + 1.333333334 = -6.912147118 Reorder the terms: 1.333333334 + x = -6.912147118 Solving 1.333333334 + x = -6.912147118 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 = -6.912147118 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -6.912147118 + -1.333333334 x = -6.912147118 + -1.333333334 Combine like terms: -6.912147118 + -1.333333334 = -8.245480452 x = -8.245480452 Simplifying x = -8.245480452Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.578813784, -8.245480452}
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