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Simplifying 0 = -1x2 + -2x + 599 Reorder the terms: 0 = 599 + -2x + -1x2 Solving 0 = 599 + -2x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -599 = -599 -599 + 2x + x2 = 599 + -2x + -1x2 + -599 + 2x + x2 Reorder the terms: -599 + 2x + x2 = 599 + -599 + -2x + 2x + -1x2 + x2 Combine like terms: 599 + -599 = 0 -599 + 2x + x2 = 0 + -2x + 2x + -1x2 + x2 -599 + 2x + x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 -599 + 2x + x2 = 0 + -1x2 + x2 -599 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -599 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '599' to each side of the equation. -599 + 2x + 599 + x2 = 0 + 599 Reorder the terms: -599 + 599 + 2x + x2 = 0 + 599 Combine like terms: -599 + 599 = 0 0 + 2x + x2 = 0 + 599 2x + x2 = 0 + 599 Combine like terms: 0 + 599 = 599 2x + x2 = 599 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 = 599 + 1 Reorder the terms: 1 + 2x + x2 = 599 + 1 Combine like terms: 599 + 1 = 600 1 + 2x + x2 = 600 Factor a perfect square on the left side: (x + 1)(x + 1) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + 1) equal to 24.494897428 and -24.494897428.Subproblem 1
x + 1 = 24.494897428 Simplifying x + 1 = 24.494897428 Reorder the terms: 1 + x = 24.494897428 Solving 1 + x = 24.494897428 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 = 24.494897428 + -1 Combine like terms: 1 + -1 = 0 0 + x = 24.494897428 + -1 x = 24.494897428 + -1 Combine like terms: 24.494897428 + -1 = 23.494897428 x = 23.494897428 Simplifying x = 23.494897428Subproblem 2
x + 1 = -24.494897428 Simplifying x + 1 = -24.494897428 Reorder the terms: 1 + x = -24.494897428 Solving 1 + x = -24.494897428 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 = -24.494897428 + -1 Combine like terms: 1 + -1 = 0 0 + x = -24.494897428 + -1 x = -24.494897428 + -1 Combine like terms: -24.494897428 + -1 = -25.494897428 x = -25.494897428 Simplifying x = -25.494897428Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.494897428, -25.494897428}
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