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Simplifying 3x2 + 2x + -324 = 0 Reorder the terms: -324 + 2x + 3x2 = 0 Solving -324 + 2x + 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'. -108 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 0.6666666667x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 0.6666666667x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 0.6666666667x + x2 = 0 + 108 0.6666666667x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 0.6666666667x + x2 = 108 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 = 108 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 108 + 0.1111111112 Combine like terms: 108 + 0.1111111112 = 108.1111111112 0.1111111112 + 0.6666666667x + x2 = 108.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 108.1111111112 Calculate the square root of the right side: 10.397649307 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 10.397649307 and -10.397649307.Subproblem 1
x + 0.3333333334 = 10.397649307 Simplifying x + 0.3333333334 = 10.397649307 Reorder the terms: 0.3333333334 + x = 10.397649307 Solving 0.3333333334 + x = 10.397649307 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 = 10.397649307 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 10.397649307 + -0.3333333334 x = 10.397649307 + -0.3333333334 Combine like terms: 10.397649307 + -0.3333333334 = 10.0643159736 x = 10.0643159736 Simplifying x = 10.0643159736Subproblem 2
x + 0.3333333334 = -10.397649307 Simplifying x + 0.3333333334 = -10.397649307 Reorder the terms: 0.3333333334 + x = -10.397649307 Solving 0.3333333334 + x = -10.397649307 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 = -10.397649307 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -10.397649307 + -0.3333333334 x = -10.397649307 + -0.3333333334 Combine like terms: -10.397649307 + -0.3333333334 = -10.7309826404 x = -10.7309826404 Simplifying x = -10.7309826404Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.0643159736, -10.7309826404}
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