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Simplifying 1728 + 84x + x2 = 169 Solving 1728 + 84x + x2 = 169 Solving for variable 'x'. Reorder the terms: 1728 + -169 + 84x + x2 = 169 + -169 Combine like terms: 1728 + -169 = 1559 1559 + 84x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 1559 + 84x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1559' to each side of the equation. 1559 + 84x + -1559 + x2 = 0 + -1559 Reorder the terms: 1559 + -1559 + 84x + x2 = 0 + -1559 Combine like terms: 1559 + -1559 = 0 0 + 84x + x2 = 0 + -1559 84x + x2 = 0 + -1559 Combine like terms: 0 + -1559 = -1559 84x + x2 = -1559 The x term is 84x. Take half its coefficient (42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. 84x + 1764 + x2 = -1559 + 1764 Reorder the terms: 1764 + 84x + x2 = -1559 + 1764 Combine like terms: -1559 + 1764 = 205 1764 + 84x + x2 = 205 Factor a perfect square on the left side: (x + 42)(x + 42) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 42) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 42 = 14.317821063 Simplifying x + 42 = 14.317821063 Reorder the terms: 42 + x = 14.317821063 Solving 42 + x = 14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = 14.317821063 + -42 Combine like terms: 42 + -42 = 0 0 + x = 14.317821063 + -42 x = 14.317821063 + -42 Combine like terms: 14.317821063 + -42 = -27.682178937 x = -27.682178937 Simplifying x = -27.682178937Subproblem 2
x + 42 = -14.317821063 Simplifying x + 42 = -14.317821063 Reorder the terms: 42 + x = -14.317821063 Solving 42 + x = -14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = -14.317821063 + -42 Combine like terms: 42 + -42 = 0 0 + x = -14.317821063 + -42 x = -14.317821063 + -42 Combine like terms: -14.317821063 + -42 = -56.317821063 x = -56.317821063 Simplifying x = -56.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {-27.682178937, -56.317821063}
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