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Simplifying 7x2 = 7 + -8x Solving 7x2 = 7 + -8x Solving for variable 'x'. Reorder the terms: -7 + 8x + 7x2 = 7 + -8x + -7 + 8x Reorder the terms: -7 + 8x + 7x2 = 7 + -7 + -8x + 8x Combine like terms: 7 + -7 = 0 -7 + 8x + 7x2 = 0 + -8x + 8x -7 + 8x + 7x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -7 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.142857143x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.142857143x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.142857143x + x2 = 0 + 1 1.142857143x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.142857143x + x2 = 1 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 = 1 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 1 + 0.3265306123 Combine like terms: 1 + 0.3265306123 = 1.3265306123 0.3265306123 + 1.142857143x + x2 = 1.3265306123 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 1.3265306123 Calculate the square root of the right side: 1.151751107 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 1.151751107 and -1.151751107.Subproblem 1
x + 0.5714285715 = 1.151751107 Simplifying x + 0.5714285715 = 1.151751107 Reorder the terms: 0.5714285715 + x = 1.151751107 Solving 0.5714285715 + x = 1.151751107 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 = 1.151751107 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 1.151751107 + -0.5714285715 x = 1.151751107 + -0.5714285715 Combine like terms: 1.151751107 + -0.5714285715 = 0.5803225355 x = 0.5803225355 Simplifying x = 0.5803225355Subproblem 2
x + 0.5714285715 = -1.151751107 Simplifying x + 0.5714285715 = -1.151751107 Reorder the terms: 0.5714285715 + x = -1.151751107 Solving 0.5714285715 + x = -1.151751107 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 = -1.151751107 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -1.151751107 + -0.5714285715 x = -1.151751107 + -0.5714285715 Combine like terms: -1.151751107 + -0.5714285715 = -1.7231796785 x = -1.7231796785 Simplifying x = -1.7231796785Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5803225355, -1.7231796785}
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