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Simplifying x2 + (x + 6) = 2295 Reorder the terms: x2 + (6 + x) = 2295 Remove parenthesis around (6 + x) x2 + 6 + x = 2295 Reorder the terms: 6 + x + x2 = 2295 Solving 6 + x + x2 = 2295 Solving for variable 'x'. Reorder the terms: 6 + -2295 + x + x2 = 2295 + -2295 Combine like terms: 6 + -2295 = -2289 -2289 + x + x2 = 2295 + -2295 Combine like terms: 2295 + -2295 = 0 -2289 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2289' to each side of the equation. -2289 + x + 2289 + x2 = 0 + 2289 Reorder the terms: -2289 + 2289 + x + x2 = 0 + 2289 Combine like terms: -2289 + 2289 = 0 0 + x + x2 = 0 + 2289 x + x2 = 0 + 2289 Combine like terms: 0 + 2289 = 2289 x + x2 = 2289 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 = 2289 + 0.25 Reorder the terms: 0.25 + x + x2 = 2289 + 0.25 Combine like terms: 2289 + 0.25 = 2289.25 0.25 + x + x2 = 2289.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2289.25 Calculate the square root of the right side: 47.84610747 Break this problem into two subproblems by setting (x + 0.5) equal to 47.84610747 and -47.84610747.Subproblem 1
x + 0.5 = 47.84610747 Simplifying x + 0.5 = 47.84610747 Reorder the terms: 0.5 + x = 47.84610747 Solving 0.5 + x = 47.84610747 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 = 47.84610747 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 47.84610747 + -0.5 x = 47.84610747 + -0.5 Combine like terms: 47.84610747 + -0.5 = 47.34610747 x = 47.34610747 Simplifying x = 47.34610747Subproblem 2
x + 0.5 = -47.84610747 Simplifying x + 0.5 = -47.84610747 Reorder the terms: 0.5 + x = -47.84610747 Solving 0.5 + x = -47.84610747 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 = -47.84610747 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -47.84610747 + -0.5 x = -47.84610747 + -0.5 Combine like terms: -47.84610747 + -0.5 = -48.34610747 x = -48.34610747 Simplifying x = -48.34610747Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.34610747, -48.34610747}
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