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Simplifying x2 + 22x + -140 = 0 Reorder the terms: -140 + 22x + x2 = 0 Solving -140 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 22x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 22x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 22x + x2 = 0 + 140 22x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 22x + x2 = 140 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 = 140 + 121 Reorder the terms: 121 + 22x + x2 = 140 + 121 Combine like terms: 140 + 121 = 261 121 + 22x + x2 = 261 Factor a perfect square on the left side: (x + 11)(x + 11) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (x + 11) equal to 16.155494421 and -16.155494421.Subproblem 1
x + 11 = 16.155494421 Simplifying x + 11 = 16.155494421 Reorder the terms: 11 + x = 16.155494421 Solving 11 + x = 16.155494421 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 = 16.155494421 + -11 Combine like terms: 11 + -11 = 0 0 + x = 16.155494421 + -11 x = 16.155494421 + -11 Combine like terms: 16.155494421 + -11 = 5.155494421 x = 5.155494421 Simplifying x = 5.155494421Subproblem 2
x + 11 = -16.155494421 Simplifying x + 11 = -16.155494421 Reorder the terms: 11 + x = -16.155494421 Solving 11 + x = -16.155494421 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 = -16.155494421 + -11 Combine like terms: 11 + -11 = 0 0 + x = -16.155494421 + -11 x = -16.155494421 + -11 Combine like terms: -16.155494421 + -11 = -27.155494421 x = -27.155494421 Simplifying x = -27.155494421Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.155494421, -27.155494421}
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