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Simplifying x2 + x + -2.4 = 540.8 Reorder the terms: -2.4 + x + x2 = 540.8 Solving -2.4 + x + x2 = 540.8 Solving for variable 'x'. Reorder the terms: -2.4 + -540.8 + x + x2 = 540.8 + -540.8 Combine like terms: -2.4 + -540.8 = -543.2 -543.2 + x + x2 = 540.8 + -540.8 Combine like terms: 540.8 + -540.8 = 0.0 -543.2 + x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '543.2' to each side of the equation. -543.2 + x + 543.2 + x2 = 0.0 + 543.2 Reorder the terms: -543.2 + 543.2 + x + x2 = 0.0 + 543.2 Combine like terms: -543.2 + 543.2 = 0.0 0.0 + x + x2 = 0.0 + 543.2 x + x2 = 0.0 + 543.2 Combine like terms: 0.0 + 543.2 = 543.2 x + x2 = 543.2 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. x + 0.25 + x2 = 543.2 + 0.25 Reorder the terms: 0.25 + x + x2 = 543.2 + 0.25 Combine like terms: 543.2 + 0.25 = 543.45 0.25 + x + x2 = 543.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 543.45 Calculate the square root of the right side: 23.31201407 Break this problem into two subproblems by setting (x + 0.5) equal to 23.31201407 and -23.31201407.Subproblem 1
x + 0.5 = 23.31201407 Simplifying x + 0.5 = 23.31201407 Reorder the terms: 0.5 + x = 23.31201407 Solving 0.5 + x = 23.31201407 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 = 23.31201407 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 23.31201407 + -0.5 x = 23.31201407 + -0.5 Combine like terms: 23.31201407 + -0.5 = 22.81201407 x = 22.81201407 Simplifying x = 22.81201407Subproblem 2
x + 0.5 = -23.31201407 Simplifying x + 0.5 = -23.31201407 Reorder the terms: 0.5 + x = -23.31201407 Solving 0.5 + x = -23.31201407 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 = -23.31201407 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -23.31201407 + -0.5 x = -23.31201407 + -0.5 Combine like terms: -23.31201407 + -0.5 = -23.81201407 x = -23.81201407 Simplifying x = -23.81201407Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.81201407, -23.81201407}
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