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Simplifying x2 + x = 810 Reorder the terms: x + x2 = 810 Solving x + x2 = 810 Solving for variable 'x'. Reorder the terms: -810 + x + x2 = 810 + -810 Combine like terms: 810 + -810 = 0 -810 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '810' to each side of the equation. -810 + x + 810 + x2 = 0 + 810 Reorder the terms: -810 + 810 + x + x2 = 0 + 810 Combine like terms: -810 + 810 = 0 0 + x + x2 = 0 + 810 x + x2 = 0 + 810 Combine like terms: 0 + 810 = 810 x + x2 = 810 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 = 810 + 0.25 Reorder the terms: 0.25 + x + x2 = 810 + 0.25 Combine like terms: 810 + 0.25 = 810.25 0.25 + x + x2 = 810.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 810.25 Calculate the square root of the right side: 28.464890655 Break this problem into two subproblems by setting (x + 0.5) equal to 28.464890655 and -28.464890655.Subproblem 1
x + 0.5 = 28.464890655 Simplifying x + 0.5 = 28.464890655 Reorder the terms: 0.5 + x = 28.464890655 Solving 0.5 + x = 28.464890655 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 = 28.464890655 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 28.464890655 + -0.5 x = 28.464890655 + -0.5 Combine like terms: 28.464890655 + -0.5 = 27.964890655 x = 27.964890655 Simplifying x = 27.964890655Subproblem 2
x + 0.5 = -28.464890655 Simplifying x + 0.5 = -28.464890655 Reorder the terms: 0.5 + x = -28.464890655 Solving 0.5 + x = -28.464890655 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 = -28.464890655 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -28.464890655 + -0.5 x = -28.464890655 + -0.5 Combine like terms: -28.464890655 + -0.5 = -28.964890655 x = -28.964890655 Simplifying x = -28.964890655Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.964890655, -28.964890655}
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