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Simplifying 2x + -38 + x(x + 37) = 571 Reorder the terms: 2x + -38 + x(37 + x) = 571 2x + -38 + (37 * x + x * x) = 571 2x + -38 + (37x + x2) = 571 Reorder the terms: -38 + 2x + 37x + x2 = 571 Combine like terms: 2x + 37x = 39x -38 + 39x + x2 = 571 Solving -38 + 39x + x2 = 571 Solving for variable 'x'. Reorder the terms: -38 + -571 + 39x + x2 = 571 + -571 Combine like terms: -38 + -571 = -609 -609 + 39x + x2 = 571 + -571 Combine like terms: 571 + -571 = 0 -609 + 39x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '609' to each side of the equation. -609 + 39x + 609 + x2 = 0 + 609 Reorder the terms: -609 + 609 + 39x + x2 = 0 + 609 Combine like terms: -609 + 609 = 0 0 + 39x + x2 = 0 + 609 39x + x2 = 0 + 609 Combine like terms: 0 + 609 = 609 39x + x2 = 609 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = 609 + 380.25 Reorder the terms: 380.25 + 39x + x2 = 609 + 380.25 Combine like terms: 609 + 380.25 = 989.25 380.25 + 39x + x2 = 989.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 989.25 Calculate the square root of the right side: 31.452344905 Break this problem into two subproblems by setting (x + 19.5) equal to 31.452344905 and -31.452344905.Subproblem 1
x + 19.5 = 31.452344905 Simplifying x + 19.5 = 31.452344905 Reorder the terms: 19.5 + x = 31.452344905 Solving 19.5 + x = 31.452344905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 31.452344905 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 31.452344905 + -19.5 x = 31.452344905 + -19.5 Combine like terms: 31.452344905 + -19.5 = 11.952344905 x = 11.952344905 Simplifying x = 11.952344905Subproblem 2
x + 19.5 = -31.452344905 Simplifying x + 19.5 = -31.452344905 Reorder the terms: 19.5 + x = -31.452344905 Solving 19.5 + x = -31.452344905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -31.452344905 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -31.452344905 + -19.5 x = -31.452344905 + -19.5 Combine like terms: -31.452344905 + -19.5 = -50.952344905 x = -50.952344905 Simplifying x = -50.952344905Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.952344905, -50.952344905}
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