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Simplifying x2 + 6x = 573 Reorder the terms: 6x + x2 = 573 Solving 6x + x2 = 573 Solving for variable 'x'. Reorder the terms: -573 + 6x + x2 = 573 + -573 Combine like terms: 573 + -573 = 0 -573 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '573' to each side of the equation. -573 + 6x + 573 + x2 = 0 + 573 Reorder the terms: -573 + 573 + 6x + x2 = 0 + 573 Combine like terms: -573 + 573 = 0 0 + 6x + x2 = 0 + 573 6x + x2 = 0 + 573 Combine like terms: 0 + 573 = 573 6x + x2 = 573 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 573 + 9 Reorder the terms: 9 + 6x + x2 = 573 + 9 Combine like terms: 573 + 9 = 582 9 + 6x + x2 = 582 Factor a perfect square on the left side: (x + 3)(x + 3) = 582 Calculate the square root of the right side: 24.124676164 Break this problem into two subproblems by setting (x + 3) equal to 24.124676164 and -24.124676164.Subproblem 1
x + 3 = 24.124676164 Simplifying x + 3 = 24.124676164 Reorder the terms: 3 + x = 24.124676164 Solving 3 + x = 24.124676164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 24.124676164 + -3 Combine like terms: 3 + -3 = 0 0 + x = 24.124676164 + -3 x = 24.124676164 + -3 Combine like terms: 24.124676164 + -3 = 21.124676164 x = 21.124676164 Simplifying x = 21.124676164Subproblem 2
x + 3 = -24.124676164 Simplifying x + 3 = -24.124676164 Reorder the terms: 3 + x = -24.124676164 Solving 3 + x = -24.124676164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -24.124676164 + -3 Combine like terms: 3 + -3 = 0 0 + x = -24.124676164 + -3 x = -24.124676164 + -3 Combine like terms: -24.124676164 + -3 = -27.124676164 x = -27.124676164 Simplifying x = -27.124676164Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.124676164, -27.124676164}
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