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Simplifying x2 + 20x + 98 = 0 Reorder the terms: 98 + 20x + x2 = 0 Solving 98 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + 20x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + 20x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + 20x + x2 = 0 + -98 20x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 20x + x2 = -98 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -98 + 100 Reorder the terms: 100 + 20x + x2 = -98 + 100 Combine like terms: -98 + 100 = 2 100 + 20x + x2 = 2 Factor a perfect square on the left side: (x + 10)(x + 10) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 10) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 10 = 1.414213562 Simplifying x + 10 = 1.414213562 Reorder the terms: 10 + x = 1.414213562 Solving 10 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 1.414213562 + -10 Combine like terms: 10 + -10 = 0 0 + x = 1.414213562 + -10 x = 1.414213562 + -10 Combine like terms: 1.414213562 + -10 = -8.585786438 x = -8.585786438 Simplifying x = -8.585786438Subproblem 2
x + 10 = -1.414213562 Simplifying x + 10 = -1.414213562 Reorder the terms: 10 + x = -1.414213562 Solving 10 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -1.414213562 + -10 Combine like terms: 10 + -10 = 0 0 + x = -1.414213562 + -10 x = -1.414213562 + -10 Combine like terms: -1.414213562 + -10 = -11.414213562 x = -11.414213562 Simplifying x = -11.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.585786438, -11.414213562}
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