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Simplifying x(34 + x) + (-35 + 2x) = 631 (34 * x + x * x) + (-35 + 2x) = 631 (34x + x2) + (-35 + 2x) = 631 Remove parenthesis around (-35 + 2x) 34x + x2 + -35 + 2x = 631 Reorder the terms: -35 + 34x + 2x + x2 = 631 Combine like terms: 34x + 2x = 36x -35 + 36x + x2 = 631 Solving -35 + 36x + x2 = 631 Solving for variable 'x'. Reorder the terms: -35 + -631 + 36x + x2 = 631 + -631 Combine like terms: -35 + -631 = -666 -666 + 36x + x2 = 631 + -631 Combine like terms: 631 + -631 = 0 -666 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '666' to each side of the equation. -666 + 36x + 666 + x2 = 0 + 666 Reorder the terms: -666 + 666 + 36x + x2 = 0 + 666 Combine like terms: -666 + 666 = 0 0 + 36x + x2 = 0 + 666 36x + x2 = 0 + 666 Combine like terms: 0 + 666 = 666 36x + x2 = 666 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 666 + 324 Reorder the terms: 324 + 36x + x2 = 666 + 324 Combine like terms: 666 + 324 = 990 324 + 36x + x2 = 990 Factor a perfect square on the left side: (x + 18)(x + 18) = 990 Calculate the square root of the right side: 31.464265445 Break this problem into two subproblems by setting (x + 18) equal to 31.464265445 and -31.464265445.Subproblem 1
x + 18 = 31.464265445 Simplifying x + 18 = 31.464265445 Reorder the terms: 18 + x = 31.464265445 Solving 18 + x = 31.464265445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 31.464265445 + -18 Combine like terms: 18 + -18 = 0 0 + x = 31.464265445 + -18 x = 31.464265445 + -18 Combine like terms: 31.464265445 + -18 = 13.464265445 x = 13.464265445 Simplifying x = 13.464265445Subproblem 2
x + 18 = -31.464265445 Simplifying x + 18 = -31.464265445 Reorder the terms: 18 + x = -31.464265445 Solving 18 + x = -31.464265445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -31.464265445 + -18 Combine like terms: 18 + -18 = 0 0 + x = -31.464265445 + -18 x = -31.464265445 + -18 Combine like terms: -31.464265445 + -18 = -49.464265445 x = -49.464265445 Simplifying x = -49.464265445Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.464265445, -49.464265445}
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