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Simplifying 3x2 + 2x + 1 = 331 Reorder the terms: 1 + 2x + 3x2 = 331 Solving 1 + 2x + 3x2 = 331 Solving for variable 'x'. Reorder the terms: 1 + -331 + 2x + 3x2 = 331 + -331 Combine like terms: 1 + -331 = -330 -330 + 2x + 3x2 = 331 + -331 Combine like terms: 331 + -331 = 0 -330 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -110 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 0.6666666667x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 0.6666666667x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 0.6666666667x + x2 = 0 + 110 0.6666666667x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 0.6666666667x + x2 = 110 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 = 110 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 110 + 0.1111111112 Combine like terms: 110 + 0.1111111112 = 110.1111111112 0.1111111112 + 0.6666666667x + x2 = 110.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 110.1111111112 Calculate the square root of the right side: 10.493384159 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 10.493384159 and -10.493384159.Subproblem 1
x + 0.3333333334 = 10.493384159 Simplifying x + 0.3333333334 = 10.493384159 Reorder the terms: 0.3333333334 + x = 10.493384159 Solving 0.3333333334 + x = 10.493384159 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 = 10.493384159 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 10.493384159 + -0.3333333334 x = 10.493384159 + -0.3333333334 Combine like terms: 10.493384159 + -0.3333333334 = 10.1600508256 x = 10.1600508256 Simplifying x = 10.1600508256Subproblem 2
x + 0.3333333334 = -10.493384159 Simplifying x + 0.3333333334 = -10.493384159 Reorder the terms: 0.3333333334 + x = -10.493384159 Solving 0.3333333334 + x = -10.493384159 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 = -10.493384159 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -10.493384159 + -0.3333333334 x = -10.493384159 + -0.3333333334 Combine like terms: -10.493384159 + -0.3333333334 = -10.8267174924 x = -10.8267174924 Simplifying x = -10.8267174924Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.1600508256, -10.8267174924}
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