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Simplifying x2 + 121x + 121 = 0 Reorder the terms: 121 + 121x + x2 = 0 Solving 121 + 121x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-121' to each side of the equation. 121 + 121x + -121 + x2 = 0 + -121 Reorder the terms: 121 + -121 + 121x + x2 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + 121x + x2 = 0 + -121 121x + x2 = 0 + -121 Combine like terms: 0 + -121 = -121 121x + x2 = -121 The x term is 121x. Take half its coefficient (60.5). Square it (3660.25) and add it to both sides. Add '3660.25' to each side of the equation. 121x + 3660.25 + x2 = -121 + 3660.25 Reorder the terms: 3660.25 + 121x + x2 = -121 + 3660.25 Combine like terms: -121 + 3660.25 = 3539.25 3660.25 + 121x + x2 = 3539.25 Factor a perfect square on the left side: (x + 60.5)(x + 60.5) = 3539.25 Calculate the square root of the right side: 59.491596045 Break this problem into two subproblems by setting (x + 60.5) equal to 59.491596045 and -59.491596045.Subproblem 1
x + 60.5 = 59.491596045 Simplifying x + 60.5 = 59.491596045 Reorder the terms: 60.5 + x = 59.491596045 Solving 60.5 + x = 59.491596045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + x = 59.491596045 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + x = 59.491596045 + -60.5 x = 59.491596045 + -60.5 Combine like terms: 59.491596045 + -60.5 = -1.008403955 x = -1.008403955 Simplifying x = -1.008403955Subproblem 2
x + 60.5 = -59.491596045 Simplifying x + 60.5 = -59.491596045 Reorder the terms: 60.5 + x = -59.491596045 Solving 60.5 + x = -59.491596045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + x = -59.491596045 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + x = -59.491596045 + -60.5 x = -59.491596045 + -60.5 Combine like terms: -59.491596045 + -60.5 = -119.991596045 x = -119.991596045 Simplifying x = -119.991596045Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.008403955, -119.991596045}
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