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Simplifying (3x2 + 2x + 5) + (8x2 + -8 + -8x) = 0 Reorder the terms: (5 + 2x + 3x2) + (8x2 + -8 + -8x) = 0 Remove parenthesis around (5 + 2x + 3x2) 5 + 2x + 3x2 + (8x2 + -8 + -8x) = 0 Reorder the terms: 5 + 2x + 3x2 + (-8 + -8x + 8x2) = 0 Remove parenthesis around (-8 + -8x + 8x2) 5 + 2x + 3x2 + -8 + -8x + 8x2 = 0 Reorder the terms: 5 + -8 + 2x + -8x + 3x2 + 8x2 = 0 Combine like terms: 5 + -8 = -3 -3 + 2x + -8x + 3x2 + 8x2 = 0 Combine like terms: 2x + -8x = -6x -3 + -6x + 3x2 + 8x2 = 0 Combine like terms: 3x2 + 8x2 = 11x2 -3 + -6x + 11x2 = 0 Solving -3 + -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'. -0.2727272727 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.5454545455x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.5454545455x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.5454545455x + x2 = 0 + 0.2727272727 -0.5454545455x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.5454545455x + x2 = 0.2727272727 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 = 0.2727272727 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 0.2727272727 + 0.07438016533 Combine like terms: 0.2727272727 + 0.07438016533 = 0.34710743803 0.07438016533 + -0.5454545455x + x2 = 0.34710743803 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 0.34710743803 Calculate the square root of the right side: 0.589158245 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 0.589158245 and -0.589158245.Subproblem 1
x + -0.2727272728 = 0.589158245 Simplifying x + -0.2727272728 = 0.589158245 Reorder the terms: -0.2727272728 + x = 0.589158245 Solving -0.2727272728 + x = 0.589158245 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 = 0.589158245 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 0.589158245 + 0.2727272728 x = 0.589158245 + 0.2727272728 Combine like terms: 0.589158245 + 0.2727272728 = 0.8618855178 x = 0.8618855178 Simplifying x = 0.8618855178Subproblem 2
x + -0.2727272728 = -0.589158245 Simplifying x + -0.2727272728 = -0.589158245 Reorder the terms: -0.2727272728 + x = -0.589158245 Solving -0.2727272728 + x = -0.589158245 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 = -0.589158245 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -0.589158245 + 0.2727272728 x = -0.589158245 + 0.2727272728 Combine like terms: -0.589158245 + 0.2727272728 = -0.3164309722 x = -0.3164309722 Simplifying x = -0.3164309722Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8618855178, -0.3164309722}
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