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Simplifying 3x2 + -8x + -340 = 0 Reorder the terms: -340 + -8x + 3x2 = 0 Solving -340 + -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'. -113.3333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '113.3333333' to each side of the equation. -113.3333333 + -2.666666667x + 113.3333333 + x2 = 0 + 113.3333333 Reorder the terms: -113.3333333 + 113.3333333 + -2.666666667x + x2 = 0 + 113.3333333 Combine like terms: -113.3333333 + 113.3333333 = 0.0000000 0.0000000 + -2.666666667x + x2 = 0 + 113.3333333 -2.666666667x + x2 = 0 + 113.3333333 Combine like terms: 0 + 113.3333333 = 113.3333333 -2.666666667x + x2 = 113.3333333 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 = 113.3333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 113.3333333 + 1.777777780 Combine like terms: 113.3333333 + 1.777777780 = 115.11111108 1.777777780 + -2.666666667x + x2 = 115.11111108 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 115.11111108 Calculate the square root of the right side: 10.728984625 Break this problem into two subproblems by setting (x + -1.333333334) equal to 10.728984625 and -10.728984625.Subproblem 1
x + -1.333333334 = 10.728984625 Simplifying x + -1.333333334 = 10.728984625 Reorder the terms: -1.333333334 + x = 10.728984625 Solving -1.333333334 + x = 10.728984625 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 = 10.728984625 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 10.728984625 + 1.333333334 x = 10.728984625 + 1.333333334 Combine like terms: 10.728984625 + 1.333333334 = 12.062317959 x = 12.062317959 Simplifying x = 12.062317959Subproblem 2
x + -1.333333334 = -10.728984625 Simplifying x + -1.333333334 = -10.728984625 Reorder the terms: -1.333333334 + x = -10.728984625 Solving -1.333333334 + x = -10.728984625 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 = -10.728984625 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -10.728984625 + 1.333333334 x = -10.728984625 + 1.333333334 Combine like terms: -10.728984625 + 1.333333334 = -9.395651291 x = -9.395651291 Simplifying x = -9.395651291Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.062317959, -9.395651291}
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