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Simplifying (6x2 + -2x + -6) + (5x2 + -2x + 1) = 0 Reorder the terms: (-6 + -2x + 6x2) + (5x2 + -2x + 1) = 0 Remove parenthesis around (-6 + -2x + 6x2) -6 + -2x + 6x2 + (5x2 + -2x + 1) = 0 Reorder the terms: -6 + -2x + 6x2 + (1 + -2x + 5x2) = 0 Remove parenthesis around (1 + -2x + 5x2) -6 + -2x + 6x2 + 1 + -2x + 5x2 = 0 Reorder the terms: -6 + 1 + -2x + -2x + 6x2 + 5x2 = 0 Combine like terms: -6 + 1 = -5 -5 + -2x + -2x + 6x2 + 5x2 = 0 Combine like terms: -2x + -2x = -4x -5 + -4x + 6x2 + 5x2 = 0 Combine like terms: 6x2 + 5x2 = 11x2 -5 + -4x + 11x2 = 0 Solving -5 + -4x + 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'. -0.4545454545 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.3636363636x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.3636363636x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.3636363636x + x2 = 0 + 0.4545454545 -0.3636363636x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.3636363636x + x2 = 0.4545454545 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 0.4545454545 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.4545454545 + 0.03305785123 Combine like terms: 0.4545454545 + 0.03305785123 = 0.48760330573 0.03305785123 + -0.3636363636x + x2 = 0.48760330573 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.48760330573 Calculate the square root of the right side: 0.698285977 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.698285977 and -0.698285977.Subproblem 1
x + -0.1818181818 = 0.698285977 Simplifying x + -0.1818181818 = 0.698285977 Reorder the terms: -0.1818181818 + x = 0.698285977 Solving -0.1818181818 + x = 0.698285977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 0.698285977 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.698285977 + 0.1818181818 x = 0.698285977 + 0.1818181818 Combine like terms: 0.698285977 + 0.1818181818 = 0.8801041588 x = 0.8801041588 Simplifying x = 0.8801041588Subproblem 2
x + -0.1818181818 = -0.698285977 Simplifying x + -0.1818181818 = -0.698285977 Reorder the terms: -0.1818181818 + x = -0.698285977 Solving -0.1818181818 + x = -0.698285977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -0.698285977 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.698285977 + 0.1818181818 x = -0.698285977 + 0.1818181818 Combine like terms: -0.698285977 + 0.1818181818 = -0.5164677952 x = -0.5164677952 Simplifying x = -0.5164677952Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8801041588, -0.5164677952}
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