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Simplifying x2 + 5x + -8020 = 0 Reorder the terms: -8020 + 5x + x2 = 0 Solving -8020 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8020' to each side of the equation. -8020 + 5x + 8020 + x2 = 0 + 8020 Reorder the terms: -8020 + 8020 + 5x + x2 = 0 + 8020 Combine like terms: -8020 + 8020 = 0 0 + 5x + x2 = 0 + 8020 5x + x2 = 0 + 8020 Combine like terms: 0 + 8020 = 8020 5x + x2 = 8020 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 8020 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 8020 + 6.25 Combine like terms: 8020 + 6.25 = 8026.25 6.25 + 5x + x2 = 8026.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8026.25 Calculate the square root of the right side: 89.589340884 Break this problem into two subproblems by setting (x + 2.5) equal to 89.589340884 and -89.589340884.Subproblem 1
x + 2.5 = 89.589340884 Simplifying x + 2.5 = 89.589340884 Reorder the terms: 2.5 + x = 89.589340884 Solving 2.5 + x = 89.589340884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 89.589340884 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 89.589340884 + -2.5 x = 89.589340884 + -2.5 Combine like terms: 89.589340884 + -2.5 = 87.089340884 x = 87.089340884 Simplifying x = 87.089340884Subproblem 2
x + 2.5 = -89.589340884 Simplifying x + 2.5 = -89.589340884 Reorder the terms: 2.5 + x = -89.589340884 Solving 2.5 + x = -89.589340884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -89.589340884 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -89.589340884 + -2.5 x = -89.589340884 + -2.5 Combine like terms: -89.589340884 + -2.5 = -92.089340884 x = -92.089340884 Simplifying x = -92.089340884Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.089340884, -92.089340884}
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