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Simplifying (8x2 + -3x + -7) + (3x2 + -3x + -6) = 0 Reorder the terms: (-7 + -3x + 8x2) + (3x2 + -3x + -6) = 0 Remove parenthesis around (-7 + -3x + 8x2) -7 + -3x + 8x2 + (3x2 + -3x + -6) = 0 Reorder the terms: -7 + -3x + 8x2 + (-6 + -3x + 3x2) = 0 Remove parenthesis around (-6 + -3x + 3x2) -7 + -3x + 8x2 + -6 + -3x + 3x2 = 0 Reorder the terms: -7 + -6 + -3x + -3x + 8x2 + 3x2 = 0 Combine like terms: -7 + -6 = -13 -13 + -3x + -3x + 8x2 + 3x2 = 0 Combine like terms: -3x + -3x = -6x -13 + -6x + 8x2 + 3x2 = 0 Combine like terms: 8x2 + 3x2 = 11x2 -13 + -6x + 11x2 = 0 Solving -13 + -6x + 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'. -1.181818182 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -0.5454545455x + 1.181818182 + x2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -0.5454545455x + x2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -0.5454545455x + x2 = 0 + 1.181818182 -0.5454545455x + x2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -0.5454545455x + x2 = 1.181818182 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 1.181818182 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 1.181818182 + 0.07438016533 Combine like terms: 1.181818182 + 0.07438016533 = 1.25619834733 0.07438016533 + -0.5454545455x + x2 = 1.25619834733 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 1.25619834733 Calculate the square root of the right side: 1.120802546 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 1.120802546 and -1.120802546.Subproblem 1
x + -0.2727272728 = 1.120802546 Simplifying x + -0.2727272728 = 1.120802546 Reorder the terms: -0.2727272728 + x = 1.120802546 Solving -0.2727272728 + x = 1.120802546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 1.120802546 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 1.120802546 + 0.2727272728 x = 1.120802546 + 0.2727272728 Combine like terms: 1.120802546 + 0.2727272728 = 1.3935298188 x = 1.3935298188 Simplifying x = 1.3935298188Subproblem 2
x + -0.2727272728 = -1.120802546 Simplifying x + -0.2727272728 = -1.120802546 Reorder the terms: -0.2727272728 + x = -1.120802546 Solving -0.2727272728 + x = -1.120802546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -1.120802546 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -1.120802546 + 0.2727272728 x = -1.120802546 + 0.2727272728 Combine like terms: -1.120802546 + 0.2727272728 = -0.8480752732 x = -0.8480752732 Simplifying x = -0.8480752732Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3935298188, -0.8480752732}
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