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Simplifying 3x2 + -2x + -165 = 0 Reorder the terms: -165 + -2x + 3x2 = 0 Solving -165 + -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'. -55 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -0.6666666667x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -0.6666666667x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -0.6666666667x + x2 = 0 + 55 -0.6666666667x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -0.6666666667x + x2 = 55 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 = 55 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 55 + 0.1111111112 Combine like terms: 55 + 0.1111111112 = 55.1111111112 0.1111111112 + -0.6666666667x + x2 = 55.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 55.1111111112 Calculate the square root of the right side: 7.423685817 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 7.423685817 and -7.423685817.Subproblem 1
x + -0.3333333334 = 7.423685817 Simplifying x + -0.3333333334 = 7.423685817 Reorder the terms: -0.3333333334 + x = 7.423685817 Solving -0.3333333334 + x = 7.423685817 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 = 7.423685817 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 7.423685817 + 0.3333333334 x = 7.423685817 + 0.3333333334 Combine like terms: 7.423685817 + 0.3333333334 = 7.7570191504 x = 7.7570191504 Simplifying x = 7.7570191504Subproblem 2
x + -0.3333333334 = -7.423685817 Simplifying x + -0.3333333334 = -7.423685817 Reorder the terms: -0.3333333334 + x = -7.423685817 Solving -0.3333333334 + x = -7.423685817 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 = -7.423685817 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -7.423685817 + 0.3333333334 x = -7.423685817 + 0.3333333334 Combine like terms: -7.423685817 + 0.3333333334 = -7.0903524836 x = -7.0903524836 Simplifying x = -7.0903524836Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.7570191504, -7.0903524836}
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