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Simplifying 21000 = x2 + -1x + 1 Reorder the terms: 21000 = 1 + -1x + x2 Solving 21000 = 1 + -1x + x2 Solving for variable 'x'. Combine like terms: 21000 + -1 = 20999 20999 + x + -1x2 = 1 + -1x + x2 + -1 + x + -1x2 Reorder the terms: 20999 + x + -1x2 = 1 + -1 + -1x + x + x2 + -1x2 Combine like terms: 1 + -1 = 0 20999 + x + -1x2 = 0 + -1x + x + x2 + -1x2 20999 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 20999 + x + -1x2 = 0 + x2 + -1x2 20999 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 20999 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20999 + -1x + x2 = 0 Move the constant term to the right: Add '20999' to each side of the equation. -20999 + -1x + 20999 + x2 = 0 + 20999 Reorder the terms: -20999 + 20999 + -1x + x2 = 0 + 20999 Combine like terms: -20999 + 20999 = 0 0 + -1x + x2 = 0 + 20999 -1x + x2 = 0 + 20999 Combine like terms: 0 + 20999 = 20999 -1x + x2 = 20999 The x term is x. 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 = 20999 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 20999 + 0.25 Combine like terms: 20999 + 0.25 = 20999.25 0.25 + -1x + x2 = 20999.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 20999.25 Calculate the square root of the right side: 144.911179693 Break this problem into two subproblems by setting (x + 0.5) equal to 144.911179693 and -144.911179693.Subproblem 1
x + 0.5 = 144.911179693 Simplifying x + 0.5 = 144.911179693 Reorder the terms: 0.5 + x = 144.911179693 Solving 0.5 + x = 144.911179693 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 = 144.911179693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 144.911179693 + -0.5 x = 144.911179693 + -0.5 Combine like terms: 144.911179693 + -0.5 = 144.411179693 x = 144.411179693 Simplifying x = 144.411179693Subproblem 2
x + 0.5 = -144.911179693 Simplifying x + 0.5 = -144.911179693 Reorder the terms: 0.5 + x = -144.911179693 Solving 0.5 + x = -144.911179693 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 = -144.911179693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -144.911179693 + -0.5 x = -144.911179693 + -0.5 Combine like terms: -144.911179693 + -0.5 = -145.411179693 x = -145.411179693 Simplifying x = -145.411179693Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.411179693, -145.411179693}
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