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Simplifying x2 + 29x = 525 Reorder the terms: 29x + x2 = 525 Solving 29x + x2 = 525 Solving for variable 'x'. Reorder the terms: -525 + 29x + x2 = 525 + -525 Combine like terms: 525 + -525 = 0 -525 + 29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '525' to each side of the equation. -525 + 29x + 525 + x2 = 0 + 525 Reorder the terms: -525 + 525 + 29x + x2 = 0 + 525 Combine like terms: -525 + 525 = 0 0 + 29x + x2 = 0 + 525 29x + x2 = 0 + 525 Combine like terms: 0 + 525 = 525 29x + x2 = 525 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 525 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 525 + 210.25 Combine like terms: 525 + 210.25 = 735.25 210.25 + 29x + x2 = 735.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 735.25 Calculate the square root of the right side: 27.115493726 Break this problem into two subproblems by setting (x + 14.5) equal to 27.115493726 and -27.115493726.Subproblem 1
x + 14.5 = 27.115493726 Simplifying x + 14.5 = 27.115493726 Reorder the terms: 14.5 + x = 27.115493726 Solving 14.5 + x = 27.115493726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 27.115493726 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 27.115493726 + -14.5 x = 27.115493726 + -14.5 Combine like terms: 27.115493726 + -14.5 = 12.615493726 x = 12.615493726 Simplifying x = 12.615493726Subproblem 2
x + 14.5 = -27.115493726 Simplifying x + 14.5 = -27.115493726 Reorder the terms: 14.5 + x = -27.115493726 Solving 14.5 + x = -27.115493726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -27.115493726 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -27.115493726 + -14.5 x = -27.115493726 + -14.5 Combine like terms: -27.115493726 + -14.5 = -41.615493726 x = -41.615493726 Simplifying x = -41.615493726Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.615493726, -41.615493726}
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