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Simplifying x2 + 180x + 500 = 0 Reorder the terms: 500 + 180x + x2 = 0 Solving 500 + 180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 180x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 180x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 180x + x2 = 0 + -500 180x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 180x + x2 = -500 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 = -500 + 8100 Reorder the terms: 8100 + 180x + x2 = -500 + 8100 Combine like terms: -500 + 8100 = 7600 8100 + 180x + x2 = 7600 Factor a perfect square on the left side: (x + 90)(x + 90) = 7600 Calculate the square root of the right side: 87.177978871 Break this problem into two subproblems by setting (x + 90) equal to 87.177978871 and -87.177978871.Subproblem 1
x + 90 = 87.177978871 Simplifying x + 90 = 87.177978871 Reorder the terms: 90 + x = 87.177978871 Solving 90 + x = 87.177978871 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 = 87.177978871 + -90 Combine like terms: 90 + -90 = 0 0 + x = 87.177978871 + -90 x = 87.177978871 + -90 Combine like terms: 87.177978871 + -90 = -2.822021129 x = -2.822021129 Simplifying x = -2.822021129Subproblem 2
x + 90 = -87.177978871 Simplifying x + 90 = -87.177978871 Reorder the terms: 90 + x = -87.177978871 Solving 90 + x = -87.177978871 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 = -87.177978871 + -90 Combine like terms: 90 + -90 = 0 0 + x = -87.177978871 + -90 x = -87.177978871 + -90 Combine like terms: -87.177978871 + -90 = -177.177978871 x = -177.177978871 Simplifying x = -177.177978871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.822021129, -177.177978871}
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