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Simplifying 3x2 + 8x + -165 = 0 Reorder the terms: -165 + 8x + 3x2 = 0 Solving -165 + 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'. -55 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + 2.666666667x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 2.666666667x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 2.666666667x + x2 = 0 + 55 2.666666667x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 2.666666667x + x2 = 55 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 = 55 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 55 + 1.777777780 Combine like terms: 55 + 1.777777780 = 56.77777778 1.777777780 + 2.666666667x + x2 = 56.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 56.77777778 Calculate the square root of the right side: 7.535103037 Break this problem into two subproblems by setting (x + 1.333333334) equal to 7.535103037 and -7.535103037.Subproblem 1
x + 1.333333334 = 7.535103037 Simplifying x + 1.333333334 = 7.535103037 Reorder the terms: 1.333333334 + x = 7.535103037 Solving 1.333333334 + x = 7.535103037 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 = 7.535103037 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 7.535103037 + -1.333333334 x = 7.535103037 + -1.333333334 Combine like terms: 7.535103037 + -1.333333334 = 6.201769703 x = 6.201769703 Simplifying x = 6.201769703Subproblem 2
x + 1.333333334 = -7.535103037 Simplifying x + 1.333333334 = -7.535103037 Reorder the terms: 1.333333334 + x = -7.535103037 Solving 1.333333334 + x = -7.535103037 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 = -7.535103037 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -7.535103037 + -1.333333334 x = -7.535103037 + -1.333333334 Combine like terms: -7.535103037 + -1.333333334 = -8.868436371 x = -8.868436371 Simplifying x = -8.868436371Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.201769703, -8.868436371}
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