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Simplifying x2 + 22x + 98 = 0 Reorder the terms: 98 + 22x + x2 = 0 Solving 98 + 22x + 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 + 22x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + 22x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + 22x + x2 = 0 + -98 22x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 22x + x2 = -98 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -98 + 121 Reorder the terms: 121 + 22x + x2 = -98 + 121 Combine like terms: -98 + 121 = 23 121 + 22x + x2 = 23 Factor a perfect square on the left side: (x + 11)(x + 11) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 11) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 11 = 4.795831523 Simplifying x + 11 = 4.795831523 Reorder the terms: 11 + x = 4.795831523 Solving 11 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 4.795831523 + -11 Combine like terms: 11 + -11 = 0 0 + x = 4.795831523 + -11 x = 4.795831523 + -11 Combine like terms: 4.795831523 + -11 = -6.204168477 x = -6.204168477 Simplifying x = -6.204168477Subproblem 2
x + 11 = -4.795831523 Simplifying x + 11 = -4.795831523 Reorder the terms: 11 + x = -4.795831523 Solving 11 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -4.795831523 + -11 Combine like terms: 11 + -11 = 0 0 + x = -4.795831523 + -11 x = -4.795831523 + -11 Combine like terms: -4.795831523 + -11 = -15.795831523 x = -15.795831523 Simplifying x = -15.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.204168477, -15.795831523}
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