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Simplifying 3x2 + 20x + -6 = 0 Reorder the terms: -6 + 20x + 3x2 = 0 Solving -6 + 20x + 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'. -2 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6.666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6.666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6.666666667x + x2 = 0 + 2 6.666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6.666666667x + x2 = 2 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 2 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 2 + 11.11111112 Combine like terms: 2 + 11.11111112 = 13.11111112 11.11111112 + 6.666666667x + x2 = 13.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 13.11111112 Calculate the square root of the right side: 3.620926832 Break this problem into two subproblems by setting (x + 3.333333334) equal to 3.620926832 and -3.620926832.Subproblem 1
x + 3.333333334 = 3.620926832 Simplifying x + 3.333333334 = 3.620926832 Reorder the terms: 3.333333334 + x = 3.620926832 Solving 3.333333334 + x = 3.620926832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 3.620926832 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 3.620926832 + -3.333333334 x = 3.620926832 + -3.333333334 Combine like terms: 3.620926832 + -3.333333334 = 0.287593498 x = 0.287593498 Simplifying x = 0.287593498Subproblem 2
x + 3.333333334 = -3.620926832 Simplifying x + 3.333333334 = -3.620926832 Reorder the terms: 3.333333334 + x = -3.620926832 Solving 3.333333334 + x = -3.620926832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -3.620926832 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -3.620926832 + -3.333333334 x = -3.620926832 + -3.333333334 Combine like terms: -3.620926832 + -3.333333334 = -6.954260166 x = -6.954260166 Simplifying x = -6.954260166Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.287593498, -6.954260166}
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