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Simplifying x2 + -1x + -20100 = 0 Reorder the terms: -20100 + -1x + x2 = 0 Solving -20100 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20100' to each side of the equation. -20100 + -1x + 20100 + x2 = 0 + 20100 Reorder the terms: -20100 + 20100 + -1x + x2 = 0 + 20100 Combine like terms: -20100 + 20100 = 0 0 + -1x + x2 = 0 + 20100 -1x + x2 = 0 + 20100 Combine like terms: 0 + 20100 = 20100 -1x + x2 = 20100 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 20100 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 20100 + 0.25 Combine like terms: 20100 + 0.25 = 20100.25 0.25 + -1x + x2 = 20100.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 20100.25 Calculate the square root of the right side: 141.775350467 Break this problem into two subproblems by setting (x + -0.5) equal to 141.775350467 and -141.775350467.Subproblem 1
x + -0.5 = 141.775350467 Simplifying x + -0.5 = 141.775350467 Reorder the terms: -0.5 + x = 141.775350467 Solving -0.5 + x = 141.775350467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 141.775350467 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 141.775350467 + 0.5 x = 141.775350467 + 0.5 Combine like terms: 141.775350467 + 0.5 = 142.275350467 x = 142.275350467 Simplifying x = 142.275350467Subproblem 2
x + -0.5 = -141.775350467 Simplifying x + -0.5 = -141.775350467 Reorder the terms: -0.5 + x = -141.775350467 Solving -0.5 + x = -141.775350467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -141.775350467 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -141.775350467 + 0.5 x = -141.775350467 + 0.5 Combine like terms: -141.775350467 + 0.5 = -141.275350467 x = -141.275350467 Simplifying x = -141.275350467Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.275350467, -141.275350467}
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