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Simplifying x2 + 81x + -360 = 0 Reorder the terms: -360 + 81x + x2 = 0 Solving -360 + 81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 81x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 81x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 81x + x2 = 0 + 360 81x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 81x + x2 = 360 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = 360 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 360 + 1640.25 Combine like terms: 360 + 1640.25 = 2000.25 1640.25 + 81x + x2 = 2000.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 2000.25 Calculate the square root of the right side: 44.724154548 Break this problem into two subproblems by setting (x + 40.5) equal to 44.724154548 and -44.724154548.Subproblem 1
x + 40.5 = 44.724154548 Simplifying x + 40.5 = 44.724154548 Reorder the terms: 40.5 + x = 44.724154548 Solving 40.5 + x = 44.724154548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 44.724154548 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 44.724154548 + -40.5 x = 44.724154548 + -40.5 Combine like terms: 44.724154548 + -40.5 = 4.224154548 x = 4.224154548 Simplifying x = 4.224154548Subproblem 2
x + 40.5 = -44.724154548 Simplifying x + 40.5 = -44.724154548 Reorder the terms: 40.5 + x = -44.724154548 Solving 40.5 + x = -44.724154548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -44.724154548 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -44.724154548 + -40.5 x = -44.724154548 + -40.5 Combine like terms: -44.724154548 + -40.5 = -85.224154548 x = -85.224154548 Simplifying x = -85.224154548Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.224154548, -85.224154548}
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