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Simplifying x(x + 1) = 1320 Reorder the terms: x(1 + x) = 1320 (1 * x + x * x) = 1320 (1x + x2) = 1320 Solving 1x + x2 = 1320 Solving for variable 'x'. Reorder the terms: -1320 + 1x + x2 = 1320 + -1320 Combine like terms: 1320 + -1320 = 0 -1320 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1320' to each side of the equation. -1320 + 1x + 1320 + x2 = 0 + 1320 Reorder the terms: -1320 + 1320 + 1x + x2 = 0 + 1320 Combine like terms: -1320 + 1320 = 0 0 + 1x + x2 = 0 + 1320 1x + x2 = 0 + 1320 Combine like terms: 0 + 1320 = 1320 1x + x2 = 1320 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 1320 + 0.25 Reorder the terms: 0.25 + x + x2 = 1320 + 0.25 Combine like terms: 1320 + 0.25 = 1320.25 0.25 + x + x2 = 1320.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1320.25 Calculate the square root of the right side: 36.335244598 Break this problem into two subproblems by setting (x + 0.5) equal to 36.335244598 and -36.335244598.Subproblem 1
x + 0.5 = 36.335244598 Simplifying x + 0.5 = 36.335244598 Reorder the terms: 0.5 + x = 36.335244598 Solving 0.5 + x = 36.335244598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 36.335244598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 36.335244598 + -0.5 x = 36.335244598 + -0.5 Combine like terms: 36.335244598 + -0.5 = 35.835244598 x = 35.835244598 Simplifying x = 35.835244598Subproblem 2
x + 0.5 = -36.335244598 Simplifying x + 0.5 = -36.335244598 Reorder the terms: 0.5 + x = -36.335244598 Solving 0.5 + x = -36.335244598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -36.335244598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -36.335244598 + -0.5 x = -36.335244598 + -0.5 Combine like terms: -36.335244598 + -0.5 = -36.835244598 x = -36.835244598 Simplifying x = -36.835244598Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.835244598, -36.835244598}
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