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Simplifying (x2) + 20x + -7200 = 0 x2 + 20x + -7200 = 0 Reorder the terms: -7200 + 20x + x2 = 0 Solving -7200 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7200' to each side of the equation. -7200 + 20x + 7200 + x2 = 0 + 7200 Reorder the terms: -7200 + 7200 + 20x + x2 = 0 + 7200 Combine like terms: -7200 + 7200 = 0 0 + 20x + x2 = 0 + 7200 20x + x2 = 0 + 7200 Combine like terms: 0 + 7200 = 7200 20x + x2 = 7200 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 7200 + 100 Reorder the terms: 100 + 20x + x2 = 7200 + 100 Combine like terms: 7200 + 100 = 7300 100 + 20x + x2 = 7300 Factor a perfect square on the left side: (x + 10)(x + 10) = 7300 Calculate the square root of the right side: 85.440037453 Break this problem into two subproblems by setting (x + 10) equal to 85.440037453 and -85.440037453.Subproblem 1
x + 10 = 85.440037453 Simplifying x + 10 = 85.440037453 Reorder the terms: 10 + x = 85.440037453 Solving 10 + x = 85.440037453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 85.440037453 + -10 Combine like terms: 10 + -10 = 0 0 + x = 85.440037453 + -10 x = 85.440037453 + -10 Combine like terms: 85.440037453 + -10 = 75.440037453 x = 75.440037453 Simplifying x = 75.440037453Subproblem 2
x + 10 = -85.440037453 Simplifying x + 10 = -85.440037453 Reorder the terms: 10 + x = -85.440037453 Solving 10 + x = -85.440037453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -85.440037453 + -10 Combine like terms: 10 + -10 = 0 0 + x = -85.440037453 + -10 x = -85.440037453 + -10 Combine like terms: -85.440037453 + -10 = -95.440037453 x = -95.440037453 Simplifying x = -95.440037453Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.440037453, -95.440037453}
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