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Simplifying 7x2 + -24x + 16 = 0 Reorder the terms: 16 + -24x + 7x2 = 0 Solving 16 + -24x + 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'. 2.285714286 + -3.428571429x + x2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + -3.428571429x + -2.285714286 + x2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + -3.428571429x + x2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + -3.428571429x + x2 = 0 + -2.285714286 -3.428571429x + x2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 -3.428571429x + x2 = -2.285714286 The x term is -3.428571429x. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429x + 2.938775513 + x2 = -2.285714286 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429x + x2 = -2.285714286 + 2.938775513 Combine like terms: -2.285714286 + 2.938775513 = 0.653061227 2.938775513 + -3.428571429x + x2 = 0.653061227 Factor a perfect square on the left side: (x + -1.714285715)(x + -1.714285715) = 0.653061227 Calculate the square root of the right side: 0.808122037 Break this problem into two subproblems by setting (x + -1.714285715) equal to 0.808122037 and -0.808122037.Subproblem 1
x + -1.714285715 = 0.808122037 Simplifying x + -1.714285715 = 0.808122037 Reorder the terms: -1.714285715 + x = 0.808122037 Solving -1.714285715 + x = 0.808122037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = 0.808122037 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = 0.808122037 + 1.714285715 x = 0.808122037 + 1.714285715 Combine like terms: 0.808122037 + 1.714285715 = 2.522407752 x = 2.522407752 Simplifying x = 2.522407752Subproblem 2
x + -1.714285715 = -0.808122037 Simplifying x + -1.714285715 = -0.808122037 Reorder the terms: -1.714285715 + x = -0.808122037 Solving -1.714285715 + x = -0.808122037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = -0.808122037 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = -0.808122037 + 1.714285715 x = -0.808122037 + 1.714285715 Combine like terms: -0.808122037 + 1.714285715 = 0.906163678 x = 0.906163678 Simplifying x = 0.906163678Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.522407752, 0.906163678}
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