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Simplifying (3x2 + 5x + 2) + (8x2 + -6) = 0 Reorder the terms: (2 + 5x + 3x2) + (8x2 + -6) = 0 Remove parenthesis around (2 + 5x + 3x2) 2 + 5x + 3x2 + (8x2 + -6) = 0 Reorder the terms: 2 + 5x + 3x2 + (-6 + 8x2) = 0 Remove parenthesis around (-6 + 8x2) 2 + 5x + 3x2 + -6 + 8x2 = 0 Reorder the terms: 2 + -6 + 5x + 3x2 + 8x2 = 0 Combine like terms: 2 + -6 = -4 -4 + 5x + 3x2 + 8x2 = 0 Combine like terms: 3x2 + 8x2 = 11x2 -4 + 5x + 11x2 = 0 Solving -4 + 5x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 0.4545454545x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 0.4545454545x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 0.4545454545x + x2 = 0 + 0.3636363636 0.4545454545x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 0.4545454545x + x2 = 0.3636363636 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 0.3636363636 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 0.3636363636 + 0.05165289257 Combine like terms: 0.3636363636 + 0.05165289257 = 0.41528925617 0.05165289257 + 0.4545454545x + x2 = 0.41528925617 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 0.41528925617 Calculate the square root of the right side: 0.644429404 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 0.644429404 and -0.644429404.Subproblem 1
x + 0.2272727273 = 0.644429404 Simplifying x + 0.2272727273 = 0.644429404 Reorder the terms: 0.2272727273 + x = 0.644429404 Solving 0.2272727273 + x = 0.644429404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 0.644429404 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 0.644429404 + -0.2272727273 x = 0.644429404 + -0.2272727273 Combine like terms: 0.644429404 + -0.2272727273 = 0.4171566767 x = 0.4171566767 Simplifying x = 0.4171566767Subproblem 2
x + 0.2272727273 = -0.644429404 Simplifying x + 0.2272727273 = -0.644429404 Reorder the terms: 0.2272727273 + x = -0.644429404 Solving 0.2272727273 + x = -0.644429404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -0.644429404 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -0.644429404 + -0.2272727273 x = -0.644429404 + -0.2272727273 Combine like terms: -0.644429404 + -0.2272727273 = -0.8717021313 x = -0.8717021313 Simplifying x = -0.8717021313Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4171566767, -0.8717021313}
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