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Simplifying (5x2 + -6x + 8) + (2x2 + -2x + -9) = 0 Reorder the terms: (8 + -6x + 5x2) + (2x2 + -2x + -9) = 0 Remove parenthesis around (8 + -6x + 5x2) 8 + -6x + 5x2 + (2x2 + -2x + -9) = 0 Reorder the terms: 8 + -6x + 5x2 + (-9 + -2x + 2x2) = 0 Remove parenthesis around (-9 + -2x + 2x2) 8 + -6x + 5x2 + -9 + -2x + 2x2 = 0 Reorder the terms: 8 + -9 + -6x + -2x + 5x2 + 2x2 = 0 Combine like terms: 8 + -9 = -1 -1 + -6x + -2x + 5x2 + 2x2 = 0 Combine like terms: -6x + -2x = -8x -1 + -8x + 5x2 + 2x2 = 0 Combine like terms: 5x2 + 2x2 = 7x2 -1 + -8x + 7x2 = 0 Solving -1 + -8x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.142857143x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.142857143x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.1428571429 -1.142857143x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.142857143x + x2 = 0.1428571429 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 0.1428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.1428571429 + 0.3265306123 Combine like terms: 0.1428571429 + 0.3265306123 = 0.4693877552 0.3265306123 + -1.142857143x + x2 = 0.4693877552 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.4693877552 Calculate the square root of the right side: 0.685118789 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.685118789 and -0.685118789.Subproblem 1
x + -0.5714285715 = 0.685118789 Simplifying x + -0.5714285715 = 0.685118789 Reorder the terms: -0.5714285715 + x = 0.685118789 Solving -0.5714285715 + x = 0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 0.685118789 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.685118789 + 0.5714285715 x = 0.685118789 + 0.5714285715 Combine like terms: 0.685118789 + 0.5714285715 = 1.2565473605 x = 1.2565473605 Simplifying x = 1.2565473605Subproblem 2
x + -0.5714285715 = -0.685118789 Simplifying x + -0.5714285715 = -0.685118789 Reorder the terms: -0.5714285715 + x = -0.685118789 Solving -0.5714285715 + x = -0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -0.685118789 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.685118789 + 0.5714285715 x = -0.685118789 + 0.5714285715 Combine like terms: -0.685118789 + 0.5714285715 = -0.1136902175 x = -0.1136902175 Simplifying x = -0.1136902175Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2565473605, -0.1136902175}
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