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Simplifying 0 = 3x2 + -2x + -12 Reorder the terms: 0 = -12 + -2x + 3x2 Solving 0 = -12 + -2x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + 2x + -3x2 = -12 + -2x + 3x2 + 12 + 2x + -3x2 Reorder the terms: 12 + 2x + -3x2 = -12 + 12 + -2x + 2x + 3x2 + -3x2 Combine like terms: -12 + 12 = 0 12 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2 12 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 12 + 2x + -3x2 = 0 + 3x2 + -3x2 12 + 2x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 12 + 2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6666666667x + x2 = 0 + 4 -0.6666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6666666667x + x2 = 4 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 = 4 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 4 + 0.1111111112 Combine like terms: 4 + 0.1111111112 = 4.1111111112 0.1111111112 + -0.6666666667x + x2 = 4.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 4.1111111112 Calculate the square root of the right side: 2.02758751 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.02758751 and -2.02758751.Subproblem 1
x + -0.3333333334 = 2.02758751 Simplifying x + -0.3333333334 = 2.02758751 Reorder the terms: -0.3333333334 + x = 2.02758751 Solving -0.3333333334 + x = 2.02758751 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 = 2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.02758751 + 0.3333333334 x = 2.02758751 + 0.3333333334 Combine like terms: 2.02758751 + 0.3333333334 = 2.3609208434 x = 2.3609208434 Simplifying x = 2.3609208434Subproblem 2
x + -0.3333333334 = -2.02758751 Simplifying x + -0.3333333334 = -2.02758751 Reorder the terms: -0.3333333334 + x = -2.02758751 Solving -0.3333333334 + x = -2.02758751 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 = -2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.02758751 + 0.3333333334 x = -2.02758751 + 0.3333333334 Combine like terms: -2.02758751 + 0.3333333334 = -1.6942541766 x = -1.6942541766 Simplifying x = -1.6942541766Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3609208434, -1.6942541766}
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