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Simplifying 7x2 = 5 + -8x Solving 7x2 = 5 + -8x Solving for variable 'x'. Reorder the terms: -5 + 8x + 7x2 = 5 + -8x + -5 + 8x Reorder the terms: -5 + 8x + 7x2 = 5 + -5 + -8x + 8x Combine like terms: 5 + -5 = 0 -5 + 8x + 7x2 = 0 + -8x + 8x -5 + 8x + 7x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -5 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 1.142857143x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 1.142857143x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 1.142857143x + x2 = 0 + 0.7142857143 1.142857143x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 1.142857143x + x2 = 0.7142857143 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 = 0.7142857143 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 0.7142857143 + 0.3265306123 Combine like terms: 0.7142857143 + 0.3265306123 = 1.0408163266 0.3265306123 + 1.142857143x + x2 = 1.0408163266 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 1.0408163266 Calculate the square root of the right side: 1.020204061 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 1.020204061 and -1.020204061.Subproblem 1
x + 0.5714285715 = 1.020204061 Simplifying x + 0.5714285715 = 1.020204061 Reorder the terms: 0.5714285715 + x = 1.020204061 Solving 0.5714285715 + x = 1.020204061 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 = 1.020204061 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 1.020204061 + -0.5714285715 x = 1.020204061 + -0.5714285715 Combine like terms: 1.020204061 + -0.5714285715 = 0.4487754895 x = 0.4487754895 Simplifying x = 0.4487754895Subproblem 2
x + 0.5714285715 = -1.020204061 Simplifying x + 0.5714285715 = -1.020204061 Reorder the terms: 0.5714285715 + x = -1.020204061 Solving 0.5714285715 + x = -1.020204061 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 = -1.020204061 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -1.020204061 + -0.5714285715 x = -1.020204061 + -0.5714285715 Combine like terms: -1.020204061 + -0.5714285715 = -1.5916326325 x = -1.5916326325 Simplifying x = -1.5916326325Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4487754895, -1.5916326325}
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