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Simplifying x(x + 180) = 480 Reorder the terms: x(180 + x) = 480 (180 * x + x * x) = 480 (180x + x2) = 480 Solving 180x + x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 180x + x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 180x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 180x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 180x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 180x + x2 = 0 + 480 180x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 180x + x2 = 480 The x term is 180x. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180x + 8100 + x2 = 480 + 8100 Reorder the terms: 8100 + 180x + x2 = 480 + 8100 Combine like terms: 480 + 8100 = 8580 8100 + 180x + x2 = 8580 Factor a perfect square on the left side: (x + 90)(x + 90) = 8580 Calculate the square root of the right side: 92.628289415 Break this problem into two subproblems by setting (x + 90) equal to 92.628289415 and -92.628289415.Subproblem 1
x + 90 = 92.628289415 Simplifying x + 90 = 92.628289415 Reorder the terms: 90 + x = 92.628289415 Solving 90 + x = 92.628289415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = 92.628289415 + -90 Combine like terms: 90 + -90 = 0 0 + x = 92.628289415 + -90 x = 92.628289415 + -90 Combine like terms: 92.628289415 + -90 = 2.628289415 x = 2.628289415 Simplifying x = 2.628289415Subproblem 2
x + 90 = -92.628289415 Simplifying x + 90 = -92.628289415 Reorder the terms: 90 + x = -92.628289415 Solving 90 + x = -92.628289415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = -92.628289415 + -90 Combine like terms: 90 + -90 = 0 0 + x = -92.628289415 + -90 x = -92.628289415 + -90 Combine like terms: -92.628289415 + -90 = -182.628289415 x = -182.628289415 Simplifying x = -182.628289415Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.628289415, -182.628289415}
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