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Simplifying 3x2 + 2x = 12 Reorder the terms: 2x + 3x2 = 12 Solving 2x + 3x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 2x + 3x2 = 12 + -12 Combine like terms: 12 + -12 = 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 = 1.6942541766 x = 1.6942541766 Simplifying x = 1.6942541766Subproblem 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 = -2.3609208434 x = -2.3609208434 Simplifying x = -2.3609208434Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6942541766, -2.3609208434}
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