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Simplifying x2 + 2x + -20000 = 0 Reorder the terms: -20000 + 2x + x2 = 0 Solving -20000 + 2x + 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 + 2x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + 2x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + 2x + x2 = 0 + 20000 2x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 2x + x2 = 20000 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 20000 + 1 Reorder the terms: 1 + 2x + x2 = 20000 + 1 Combine like terms: 20000 + 1 = 20001 1 + 2x + x2 = 20001 Factor a perfect square on the left side: (x + 1)(x + 1) = 20001 Calculate the square root of the right side: 141.424891727 Break this problem into two subproblems by setting (x + 1) equal to 141.424891727 and -141.424891727.Subproblem 1
x + 1 = 141.424891727 Simplifying x + 1 = 141.424891727 Reorder the terms: 1 + x = 141.424891727 Solving 1 + x = 141.424891727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 141.424891727 + -1 Combine like terms: 1 + -1 = 0 0 + x = 141.424891727 + -1 x = 141.424891727 + -1 Combine like terms: 141.424891727 + -1 = 140.424891727 x = 140.424891727 Simplifying x = 140.424891727Subproblem 2
x + 1 = -141.424891727 Simplifying x + 1 = -141.424891727 Reorder the terms: 1 + x = -141.424891727 Solving 1 + x = -141.424891727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -141.424891727 + -1 Combine like terms: 1 + -1 = 0 0 + x = -141.424891727 + -1 x = -141.424891727 + -1 Combine like terms: -141.424891727 + -1 = -142.424891727 x = -142.424891727 Simplifying x = -142.424891727Solution
The solution to the problem is based on the solutions from the subproblems. x = {140.424891727, -142.424891727}
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