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Simplifying x2 + -7x + -20000 = 0 Reorder the terms: -20000 + -7x + x2 = 0 Solving -20000 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20000' to each side of the equation. -20000 + -7x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + -7x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + -7x + x2 = 0 + 20000 -7x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 -7x + x2 = 20000 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 20000 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 20000 + 12.25 Combine like terms: 20000 + 12.25 = 20012.25 12.25 + -7x + x2 = 20012.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 20012.25 Calculate the square root of the right side: 141.464659898 Break this problem into two subproblems by setting (x + -3.5) equal to 141.464659898 and -141.464659898.Subproblem 1
x + -3.5 = 141.464659898 Simplifying x + -3.5 = 141.464659898 Reorder the terms: -3.5 + x = 141.464659898 Solving -3.5 + x = 141.464659898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 141.464659898 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 141.464659898 + 3.5 x = 141.464659898 + 3.5 Combine like terms: 141.464659898 + 3.5 = 144.964659898 x = 144.964659898 Simplifying x = 144.964659898Subproblem 2
x + -3.5 = -141.464659898 Simplifying x + -3.5 = -141.464659898 Reorder the terms: -3.5 + x = -141.464659898 Solving -3.5 + x = -141.464659898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -141.464659898 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -141.464659898 + 3.5 x = -141.464659898 + 3.5 Combine like terms: -141.464659898 + 3.5 = -137.964659898 x = -137.964659898 Simplifying x = -137.964659898Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.964659898, -137.964659898}
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