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Simplifying x2 + -20x + -4000 = 0 Reorder the terms: -4000 + -20x + x2 = 0 Solving -4000 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -20x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -20x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -20x + x2 = 0 + 4000 -20x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -20x + x2 = 4000 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 = 4000 + 100 Reorder the terms: 100 + -20x + x2 = 4000 + 100 Combine like terms: 4000 + 100 = 4100 100 + -20x + x2 = 4100 Factor a perfect square on the left side: (x + -10)(x + -10) = 4100 Calculate the square root of the right side: 64.031242374 Break this problem into two subproblems by setting (x + -10) equal to 64.031242374 and -64.031242374.Subproblem 1
x + -10 = 64.031242374 Simplifying x + -10 = 64.031242374 Reorder the terms: -10 + x = 64.031242374 Solving -10 + x = 64.031242374 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 = 64.031242374 + 10 Combine like terms: -10 + 10 = 0 0 + x = 64.031242374 + 10 x = 64.031242374 + 10 Combine like terms: 64.031242374 + 10 = 74.031242374 x = 74.031242374 Simplifying x = 74.031242374Subproblem 2
x + -10 = -64.031242374 Simplifying x + -10 = -64.031242374 Reorder the terms: -10 + x = -64.031242374 Solving -10 + x = -64.031242374 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 = -64.031242374 + 10 Combine like terms: -10 + 10 = 0 0 + x = -64.031242374 + 10 x = -64.031242374 + 10 Combine like terms: -64.031242374 + 10 = -54.031242374 x = -54.031242374 Simplifying x = -54.031242374Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.031242374, -54.031242374}
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