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Simplifying x2 + 22x = 416 Reorder the terms: 22x + x2 = 416 Solving 22x + x2 = 416 Solving for variable 'x'. Reorder the terms: -416 + 22x + x2 = 416 + -416 Combine like terms: 416 + -416 = 0 -416 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '416' to each side of the equation. -416 + 22x + 416 + x2 = 0 + 416 Reorder the terms: -416 + 416 + 22x + x2 = 0 + 416 Combine like terms: -416 + 416 = 0 0 + 22x + x2 = 0 + 416 22x + x2 = 0 + 416 Combine like terms: 0 + 416 = 416 22x + x2 = 416 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 = 416 + 121 Reorder the terms: 121 + 22x + x2 = 416 + 121 Combine like terms: 416 + 121 = 537 121 + 22x + x2 = 537 Factor a perfect square on the left side: (x + 11)(x + 11) = 537 Calculate the square root of the right side: 23.173260453 Break this problem into two subproblems by setting (x + 11) equal to 23.173260453 and -23.173260453.Subproblem 1
x + 11 = 23.173260453 Simplifying x + 11 = 23.173260453 Reorder the terms: 11 + x = 23.173260453 Solving 11 + x = 23.173260453 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 = 23.173260453 + -11 Combine like terms: 11 + -11 = 0 0 + x = 23.173260453 + -11 x = 23.173260453 + -11 Combine like terms: 23.173260453 + -11 = 12.173260453 x = 12.173260453 Simplifying x = 12.173260453Subproblem 2
x + 11 = -23.173260453 Simplifying x + 11 = -23.173260453 Reorder the terms: 11 + x = -23.173260453 Solving 11 + x = -23.173260453 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 = -23.173260453 + -11 Combine like terms: 11 + -11 = 0 0 + x = -23.173260453 + -11 x = -23.173260453 + -11 Combine like terms: -23.173260453 + -11 = -34.173260453 x = -34.173260453 Simplifying x = -34.173260453Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.173260453, -34.173260453}
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