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Simplifying x2 + 29x + 53 = 0 Reorder the terms: 53 + 29x + x2 = 0 Solving 53 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 29x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 29x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 29x + x2 = 0 + -53 29x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 29x + x2 = -53 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 = -53 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -53 + 210.25 Combine like terms: -53 + 210.25 = 157.25 210.25 + 29x + x2 = 157.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 157.25 Calculate the square root of the right side: 12.539936204 Break this problem into two subproblems by setting (x + 14.5) equal to 12.539936204 and -12.539936204.Subproblem 1
x + 14.5 = 12.539936204 Simplifying x + 14.5 = 12.539936204 Reorder the terms: 14.5 + x = 12.539936204 Solving 14.5 + x = 12.539936204 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 = 12.539936204 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 12.539936204 + -14.5 x = 12.539936204 + -14.5 Combine like terms: 12.539936204 + -14.5 = -1.960063796 x = -1.960063796 Simplifying x = -1.960063796Subproblem 2
x + 14.5 = -12.539936204 Simplifying x + 14.5 = -12.539936204 Reorder the terms: 14.5 + x = -12.539936204 Solving 14.5 + x = -12.539936204 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 = -12.539936204 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -12.539936204 + -14.5 x = -12.539936204 + -14.5 Combine like terms: -12.539936204 + -14.5 = -27.039936204 x = -27.039936204 Simplifying x = -27.039936204Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.960063796, -27.039936204}
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