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Simplifying x2 + 69x + 1 = 0 Reorder the terms: 1 + 69x + x2 = 0 Solving 1 + 69x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 69x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 69x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 69x + x2 = 0 + -1 69x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 69x + x2 = -1 The x term is 69x. Take half its coefficient (34.5). Square it (1190.25) and add it to both sides. Add '1190.25' to each side of the equation. 69x + 1190.25 + x2 = -1 + 1190.25 Reorder the terms: 1190.25 + 69x + x2 = -1 + 1190.25 Combine like terms: -1 + 1190.25 = 1189.25 1190.25 + 69x + x2 = 1189.25 Factor a perfect square on the left side: (x + 34.5)(x + 34.5) = 1189.25 Calculate the square root of the right side: 34.485504201 Break this problem into two subproblems by setting (x + 34.5) equal to 34.485504201 and -34.485504201.Subproblem 1
x + 34.5 = 34.485504201 Simplifying x + 34.5 = 34.485504201 Reorder the terms: 34.5 + x = 34.485504201 Solving 34.5 + x = 34.485504201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = 34.485504201 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = 34.485504201 + -34.5 x = 34.485504201 + -34.5 Combine like terms: 34.485504201 + -34.5 = -0.014495799 x = -0.014495799 Simplifying x = -0.014495799Subproblem 2
x + 34.5 = -34.485504201 Simplifying x + 34.5 = -34.485504201 Reorder the terms: 34.5 + x = -34.485504201 Solving 34.5 + x = -34.485504201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = -34.485504201 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = -34.485504201 + -34.5 x = -34.485504201 + -34.5 Combine like terms: -34.485504201 + -34.5 = -68.985504201 x = -68.985504201 Simplifying x = -68.985504201Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.014495799, -68.985504201}
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