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Simplifying x2 + 22x = 98 Reorder the terms: 22x + x2 = 98 Solving 22x + x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 22x + x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 22x + x2 = 0 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 = 219 121 + 22x + x2 = 219 Factor a perfect square on the left side: (x + 11)(x + 11) = 219 Calculate the square root of the right side: 14.798648587 Break this problem into two subproblems by setting (x + 11) equal to 14.798648587 and -14.798648587.Subproblem 1
x + 11 = 14.798648587 Simplifying x + 11 = 14.798648587 Reorder the terms: 11 + x = 14.798648587 Solving 11 + x = 14.798648587 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 = 14.798648587 + -11 Combine like terms: 11 + -11 = 0 0 + x = 14.798648587 + -11 x = 14.798648587 + -11 Combine like terms: 14.798648587 + -11 = 3.798648587 x = 3.798648587 Simplifying x = 3.798648587Subproblem 2
x + 11 = -14.798648587 Simplifying x + 11 = -14.798648587 Reorder the terms: 11 + x = -14.798648587 Solving 11 + x = -14.798648587 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 = -14.798648587 + -11 Combine like terms: 11 + -11 = 0 0 + x = -14.798648587 + -11 x = -14.798648587 + -11 Combine like terms: -14.798648587 + -11 = -25.798648587 x = -25.798648587 Simplifying x = -25.798648587Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.798648587, -25.798648587}
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