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Simplifying x2 = 29x + 244 Reorder the terms: x2 = 244 + 29x Solving x2 = 244 + 29x Solving for variable 'x'. Reorder the terms: -244 + -29x + x2 = 244 + 29x + -244 + -29x Reorder the terms: -244 + -29x + x2 = 244 + -244 + 29x + -29x Combine like terms: 244 + -244 = 0 -244 + -29x + x2 = 0 + 29x + -29x -244 + -29x + x2 = 29x + -29x Combine like terms: 29x + -29x = 0 -244 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '244' to each side of the equation. -244 + -29x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + -29x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + -29x + x2 = 0 + 244 -29x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 -29x + x2 = 244 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 = 244 + 210.25 Reorder the terms: 210.25 + -29x + x2 = 244 + 210.25 Combine like terms: 244 + 210.25 = 454.25 210.25 + -29x + x2 = 454.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 454.25 Calculate the square root of the right side: 21.313141486 Break this problem into two subproblems by setting (x + -14.5) equal to 21.313141486 and -21.313141486.Subproblem 1
x + -14.5 = 21.313141486 Simplifying x + -14.5 = 21.313141486 Reorder the terms: -14.5 + x = 21.313141486 Solving -14.5 + x = 21.313141486 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 = 21.313141486 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 21.313141486 + 14.5 x = 21.313141486 + 14.5 Combine like terms: 21.313141486 + 14.5 = 35.813141486 x = 35.813141486 Simplifying x = 35.813141486Subproblem 2
x + -14.5 = -21.313141486 Simplifying x + -14.5 = -21.313141486 Reorder the terms: -14.5 + x = -21.313141486 Solving -14.5 + x = -21.313141486 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 = -21.313141486 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -21.313141486 + 14.5 x = -21.313141486 + 14.5 Combine like terms: -21.313141486 + 14.5 = -6.813141486 x = -6.813141486 Simplifying x = -6.813141486Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.813141486, -6.813141486}
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