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Simplifying x2 + (x + 2) = 580 Reorder the terms: x2 + (2 + x) = 580 Remove parenthesis around (2 + x) x2 + 2 + x = 580 Reorder the terms: 2 + x + x2 = 580 Solving 2 + x + x2 = 580 Solving for variable 'x'. Reorder the terms: 2 + -580 + x + x2 = 580 + -580 Combine like terms: 2 + -580 = -578 -578 + x + x2 = 580 + -580 Combine like terms: 580 + -580 = 0 -578 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '578' to each side of the equation. -578 + x + 578 + x2 = 0 + 578 Reorder the terms: -578 + 578 + x + x2 = 0 + 578 Combine like terms: -578 + 578 = 0 0 + x + x2 = 0 + 578 x + x2 = 0 + 578 Combine like terms: 0 + 578 = 578 x + x2 = 578 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 = 578 + 0.25 Reorder the terms: 0.25 + x + x2 = 578 + 0.25 Combine like terms: 578 + 0.25 = 578.25 0.25 + x + x2 = 578.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 578.25 Calculate the square root of the right side: 24.046829313 Break this problem into two subproblems by setting (x + 0.5) equal to 24.046829313 and -24.046829313.Subproblem 1
x + 0.5 = 24.046829313 Simplifying x + 0.5 = 24.046829313 Reorder the terms: 0.5 + x = 24.046829313 Solving 0.5 + x = 24.046829313 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 = 24.046829313 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 24.046829313 + -0.5 x = 24.046829313 + -0.5 Combine like terms: 24.046829313 + -0.5 = 23.546829313 x = 23.546829313 Simplifying x = 23.546829313Subproblem 2
x + 0.5 = -24.046829313 Simplifying x + 0.5 = -24.046829313 Reorder the terms: 0.5 + x = -24.046829313 Solving 0.5 + x = -24.046829313 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 = -24.046829313 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -24.046829313 + -0.5 x = -24.046829313 + -0.5 Combine like terms: -24.046829313 + -0.5 = -24.546829313 x = -24.546829313 Simplifying x = -24.546829313Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.546829313, -24.546829313}
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