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Simplifying 9x3 + 6x2 + -119x = 0 Reorder the terms: -119x + 6x2 + 9x3 = 0 Solving -119x + 6x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-119 + 6x + 9x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-119 + 6x + 9x2)' equal to zero and attempt to solve: Simplifying -119 + 6x + 9x2 = 0 Solving -119 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -13.22222222 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '13.22222222' to each side of the equation. -13.22222222 + 0.6666666667x + 13.22222222 + x2 = 0 + 13.22222222 Reorder the terms: -13.22222222 + 13.22222222 + 0.6666666667x + x2 = 0 + 13.22222222 Combine like terms: -13.22222222 + 13.22222222 = 0.00000000 0.00000000 + 0.6666666667x + x2 = 0 + 13.22222222 0.6666666667x + x2 = 0 + 13.22222222 Combine like terms: 0 + 13.22222222 = 13.22222222 0.6666666667x + x2 = 13.22222222 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 13.22222222 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 13.22222222 + 0.1111111112 Combine like terms: 13.22222222 + 0.1111111112 = 13.3333333312 0.1111111112 + 0.6666666667x + x2 = 13.3333333312 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 13.3333333312 Calculate the square root of the right side: 3.651483716 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.651483716 and -3.651483716.Subproblem 1
x + 0.3333333334 = 3.651483716 Simplifying x + 0.3333333334 = 3.651483716 Reorder the terms: 0.3333333334 + x = 3.651483716 Solving 0.3333333334 + x = 3.651483716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 3.651483716 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.651483716 + -0.3333333334 x = 3.651483716 + -0.3333333334 Combine like terms: 3.651483716 + -0.3333333334 = 3.3181503826 x = 3.3181503826 Simplifying x = 3.3181503826Subproblem 2
x + 0.3333333334 = -3.651483716 Simplifying x + 0.3333333334 = -3.651483716 Reorder the terms: 0.3333333334 + x = -3.651483716 Solving 0.3333333334 + x = -3.651483716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -3.651483716 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.651483716 + -0.3333333334 x = -3.651483716 + -0.3333333334 Combine like terms: -3.651483716 + -0.3333333334 = -3.9848170494 x = -3.9848170494 Simplifying x = -3.9848170494Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3181503826, -3.9848170494}Solution
x = {0, 3.3181503826, -3.9848170494}
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