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Simplifying 3x2 + -8x + 4 = 768 Reorder the terms: 4 + -8x + 3x2 = 768 Solving 4 + -8x + 3x2 = 768 Solving for variable 'x'. Reorder the terms: 4 + -768 + -8x + 3x2 = 768 + -768 Combine like terms: 4 + -768 = -764 -764 + -8x + 3x2 = 768 + -768 Combine like terms: 768 + -768 = 0 -764 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -254.6666667 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '254.6666667' to each side of the equation. -254.6666667 + -2.666666667x + 254.6666667 + x2 = 0 + 254.6666667 Reorder the terms: -254.6666667 + 254.6666667 + -2.666666667x + x2 = 0 + 254.6666667 Combine like terms: -254.6666667 + 254.6666667 = 0.0000000 0.0000000 + -2.666666667x + x2 = 0 + 254.6666667 -2.666666667x + x2 = 0 + 254.6666667 Combine like terms: 0 + 254.6666667 = 254.6666667 -2.666666667x + x2 = 254.6666667 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 = 254.6666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 254.6666667 + 1.777777780 Combine like terms: 254.6666667 + 1.777777780 = 256.44444448 1.777777780 + -2.666666667x + x2 = 256.44444448 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 256.44444448 Calculate the square root of the right side: 16.013882867 Break this problem into two subproblems by setting (x + -1.333333334) equal to 16.013882867 and -16.013882867.Subproblem 1
x + -1.333333334 = 16.013882867 Simplifying x + -1.333333334 = 16.013882867 Reorder the terms: -1.333333334 + x = 16.013882867 Solving -1.333333334 + x = 16.013882867 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 = 16.013882867 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 16.013882867 + 1.333333334 x = 16.013882867 + 1.333333334 Combine like terms: 16.013882867 + 1.333333334 = 17.347216201 x = 17.347216201 Simplifying x = 17.347216201Subproblem 2
x + -1.333333334 = -16.013882867 Simplifying x + -1.333333334 = -16.013882867 Reorder the terms: -1.333333334 + x = -16.013882867 Solving -1.333333334 + x = -16.013882867 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 = -16.013882867 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -16.013882867 + 1.333333334 x = -16.013882867 + 1.333333334 Combine like terms: -16.013882867 + 1.333333334 = -14.680549533 x = -14.680549533 Simplifying x = -14.680549533Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.347216201, -14.680549533}
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