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Simplifying 7x2 = 8x + 16 Reorder the terms: 7x2 = 16 + 8x Solving 7x2 = 16 + 8x Solving for variable 'x'. Reorder the terms: -16 + -8x + 7x2 = 16 + 8x + -16 + -8x Reorder the terms: -16 + -8x + 7x2 = 16 + -16 + 8x + -8x Combine like terms: 16 + -16 = 0 -16 + -8x + 7x2 = 0 + 8x + -8x -16 + -8x + 7x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -16 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -1.142857143x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -1.142857143x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 2.285714286 -1.142857143x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -1.142857143x + x2 = 2.285714286 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 = 2.285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 2.285714286 + 0.3265306123 Combine like terms: 2.285714286 + 0.3265306123 = 2.6122448983 0.3265306123 + -1.142857143x + x2 = 2.6122448983 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 2.6122448983 Calculate the square root of the right side: 1.616244071 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.616244071 and -1.616244071.Subproblem 1
x + -0.5714285715 = 1.616244071 Simplifying x + -0.5714285715 = 1.616244071 Reorder the terms: -0.5714285715 + x = 1.616244071 Solving -0.5714285715 + x = 1.616244071 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 = 1.616244071 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.616244071 + 0.5714285715 x = 1.616244071 + 0.5714285715 Combine like terms: 1.616244071 + 0.5714285715 = 2.1876726425 x = 2.1876726425 Simplifying x = 2.1876726425Subproblem 2
x + -0.5714285715 = -1.616244071 Simplifying x + -0.5714285715 = -1.616244071 Reorder the terms: -0.5714285715 + x = -1.616244071 Solving -0.5714285715 + x = -1.616244071 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 = -1.616244071 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.616244071 + 0.5714285715 x = -1.616244071 + 0.5714285715 Combine like terms: -1.616244071 + 0.5714285715 = -1.0448154995 x = -1.0448154995 Simplifying x = -1.0448154995Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1876726425, -1.0448154995}
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