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Simplifying 3x2 + -8x + -234 = 0 Reorder the terms: -234 + -8x + 3x2 = 0 Solving -234 + -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'. -78 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '78' to each side of the equation. -78 + -2.666666667x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -2.666666667x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -2.666666667x + x2 = 0 + 78 -2.666666667x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -2.666666667x + x2 = 78 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 = 78 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 78 + 1.777777780 Combine like terms: 78 + 1.777777780 = 79.77777778 1.777777780 + -2.666666667x + x2 = 79.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 79.77777778 Calculate the square root of the right side: 8.931840671 Break this problem into two subproblems by setting (x + -1.333333334) equal to 8.931840671 and -8.931840671.Subproblem 1
x + -1.333333334 = 8.931840671 Simplifying x + -1.333333334 = 8.931840671 Reorder the terms: -1.333333334 + x = 8.931840671 Solving -1.333333334 + x = 8.931840671 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 = 8.931840671 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 8.931840671 + 1.333333334 x = 8.931840671 + 1.333333334 Combine like terms: 8.931840671 + 1.333333334 = 10.265174005 x = 10.265174005 Simplifying x = 10.265174005Subproblem 2
x + -1.333333334 = -8.931840671 Simplifying x + -1.333333334 = -8.931840671 Reorder the terms: -1.333333334 + x = -8.931840671 Solving -1.333333334 + x = -8.931840671 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 = -8.931840671 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -8.931840671 + 1.333333334 x = -8.931840671 + 1.333333334 Combine like terms: -8.931840671 + 1.333333334 = -7.598507337 x = -7.598507337 Simplifying x = -7.598507337Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.265174005, -7.598507337}
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