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Simplifying 3x2 + 8x + -30 = 0 Reorder the terms: -30 + 8x + 3x2 = 0 Solving -30 + 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'. -10 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.666666667x + x2 = 0 + 10 2.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.666666667x + x2 = 10 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 = 10 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 10 + 1.777777780 Combine like terms: 10 + 1.777777780 = 11.77777778 1.777777780 + 2.666666667x + x2 = 11.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 11.77777778 Calculate the square root of the right side: 3.431876714 Break this problem into two subproblems by setting (x + 1.333333334) equal to 3.431876714 and -3.431876714.Subproblem 1
x + 1.333333334 = 3.431876714 Simplifying x + 1.333333334 = 3.431876714 Reorder the terms: 1.333333334 + x = 3.431876714 Solving 1.333333334 + x = 3.431876714 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 = 3.431876714 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 3.431876714 + -1.333333334 x = 3.431876714 + -1.333333334 Combine like terms: 3.431876714 + -1.333333334 = 2.09854338 x = 2.09854338 Simplifying x = 2.09854338Subproblem 2
x + 1.333333334 = -3.431876714 Simplifying x + 1.333333334 = -3.431876714 Reorder the terms: 1.333333334 + x = -3.431876714 Solving 1.333333334 + x = -3.431876714 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 = -3.431876714 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -3.431876714 + -1.333333334 x = -3.431876714 + -1.333333334 Combine like terms: -3.431876714 + -1.333333334 = -4.765210048 x = -4.765210048 Simplifying x = -4.765210048Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.09854338, -4.765210048}
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