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Simplifying 2x = 9 + -3x2 Solving 2x = 9 + -3x2 Solving for variable 'x'. Reorder the terms: -9 + 2x + 3x2 = 9 + -3x2 + -9 + 3x2 Reorder the terms: -9 + 2x + 3x2 = 9 + -9 + -3x2 + 3x2 Combine like terms: 9 + -9 = 0 -9 + 2x + 3x2 = 0 + -3x2 + 3x2 -9 + 2x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -9 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.6666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.6666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.6666666667x + x2 = 0 + 3 0.6666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.6666666667x + x2 = 3 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 = 3 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 3 + 0.1111111112 Combine like terms: 3 + 0.1111111112 = 3.1111111112 0.1111111112 + 0.6666666667x + x2 = 3.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 3.1111111112 Calculate the square root of the right side: 1.763834207 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.763834207 and -1.763834207.Subproblem 1
x + 0.3333333334 = 1.763834207 Simplifying x + 0.3333333334 = 1.763834207 Reorder the terms: 0.3333333334 + x = 1.763834207 Solving 0.3333333334 + x = 1.763834207 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 = 1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.763834207 + -0.3333333334 x = 1.763834207 + -0.3333333334 Combine like terms: 1.763834207 + -0.3333333334 = 1.4305008736 x = 1.4305008736 Simplifying x = 1.4305008736Subproblem 2
x + 0.3333333334 = -1.763834207 Simplifying x + 0.3333333334 = -1.763834207 Reorder the terms: 0.3333333334 + x = -1.763834207 Solving 0.3333333334 + x = -1.763834207 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 = -1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.763834207 + -0.3333333334 x = -1.763834207 + -0.3333333334 Combine like terms: -1.763834207 + -0.3333333334 = -2.0971675404 x = -2.0971675404 Simplifying x = -2.0971675404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4305008736, -2.0971675404}
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