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Simplifying 3x2 + 20x + -33 = 0 Reorder the terms: -33 + 20x + 3x2 = 0 Solving -33 + 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'. -11 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6.666666667x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 6.666666667x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6.666666667x + x2 = 0 + 11 6.666666667x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 6.666666667x + x2 = 11 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 = 11 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 11 + 11.11111112 Combine like terms: 11 + 11.11111112 = 22.11111112 11.11111112 + 6.666666667x + x2 = 22.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 22.11111112 Calculate the square root of the right side: 4.702245328 Break this problem into two subproblems by setting (x + 3.333333334) equal to 4.702245328 and -4.702245328.Subproblem 1
x + 3.333333334 = 4.702245328 Simplifying x + 3.333333334 = 4.702245328 Reorder the terms: 3.333333334 + x = 4.702245328 Solving 3.333333334 + x = 4.702245328 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 = 4.702245328 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 4.702245328 + -3.333333334 x = 4.702245328 + -3.333333334 Combine like terms: 4.702245328 + -3.333333334 = 1.368911994 x = 1.368911994 Simplifying x = 1.368911994Subproblem 2
x + 3.333333334 = -4.702245328 Simplifying x + 3.333333334 = -4.702245328 Reorder the terms: 3.333333334 + x = -4.702245328 Solving 3.333333334 + x = -4.702245328 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 = -4.702245328 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -4.702245328 + -3.333333334 x = -4.702245328 + -3.333333334 Combine like terms: -4.702245328 + -3.333333334 = -8.035578662 x = -8.035578662 Simplifying x = -8.035578662Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.368911994, -8.035578662}
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