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Simplifying 3x2 + 2x = 333 Reorder the terms: 2x + 3x2 = 333 Solving 2x + 3x2 = 333 Solving for variable 'x'. Reorder the terms: -333 + 2x + 3x2 = 333 + -333 Combine like terms: 333 + -333 = 0 -333 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -111 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '111' to each side of the equation. -111 + 0.6666666667x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + 0.6666666667x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 0.6666666667x + x2 = 0 + 111 0.6666666667x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 0.6666666667x + x2 = 111 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 = 111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 111 + 0.1111111112 Combine like terms: 111 + 0.1111111112 = 111.1111111112 0.1111111112 + 0.6666666667x + x2 = 111.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 111.1111111112 Calculate the square root of the right side: 10.540925534 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 10.540925534 and -10.540925534.Subproblem 1
x + 0.3333333334 = 10.540925534 Simplifying x + 0.3333333334 = 10.540925534 Reorder the terms: 0.3333333334 + x = 10.540925534 Solving 0.3333333334 + x = 10.540925534 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 = 10.540925534 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 10.540925534 + -0.3333333334 x = 10.540925534 + -0.3333333334 Combine like terms: 10.540925534 + -0.3333333334 = 10.2075922006 x = 10.2075922006 Simplifying x = 10.2075922006Subproblem 2
x + 0.3333333334 = -10.540925534 Simplifying x + 0.3333333334 = -10.540925534 Reorder the terms: 0.3333333334 + x = -10.540925534 Solving 0.3333333334 + x = -10.540925534 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 = -10.540925534 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -10.540925534 + -0.3333333334 x = -10.540925534 + -0.3333333334 Combine like terms: -10.540925534 + -0.3333333334 = -10.8742588674 x = -10.8742588674 Simplifying x = -10.8742588674Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.2075922006, -10.8742588674}
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