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Simplifying x2 + 29x + 59 = 0 Reorder the terms: 59 + 29x + x2 = 0 Solving 59 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 29x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 29x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 29x + x2 = 0 + -59 29x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 29x + x2 = -59 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 = -59 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -59 + 210.25 Combine like terms: -59 + 210.25 = 151.25 210.25 + 29x + x2 = 151.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 151.25 Calculate the square root of the right side: 12.298373876 Break this problem into two subproblems by setting (x + 14.5) equal to 12.298373876 and -12.298373876.Subproblem 1
x + 14.5 = 12.298373876 Simplifying x + 14.5 = 12.298373876 Reorder the terms: 14.5 + x = 12.298373876 Solving 14.5 + x = 12.298373876 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 = 12.298373876 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 12.298373876 + -14.5 x = 12.298373876 + -14.5 Combine like terms: 12.298373876 + -14.5 = -2.201626124 x = -2.201626124 Simplifying x = -2.201626124Subproblem 2
x + 14.5 = -12.298373876 Simplifying x + 14.5 = -12.298373876 Reorder the terms: 14.5 + x = -12.298373876 Solving 14.5 + x = -12.298373876 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 = -12.298373876 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -12.298373876 + -14.5 x = -12.298373876 + -14.5 Combine like terms: -12.298373876 + -14.5 = -26.798373876 x = -26.798373876 Simplifying x = -26.798373876Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.201626124, -26.798373876}
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