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Simplifying 0 = x2 + 22x + 49 Reorder the terms: 0 = 49 + 22x + x2 Solving 0 = 49 + 22x + x2 Solving for variable 'x'. Combine like terms: 0 + -49 = -49 -49 + -22x + -1x2 = 49 + 22x + x2 + -49 + -22x + -1x2 Reorder the terms: -49 + -22x + -1x2 = 49 + -49 + 22x + -22x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -49 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2 -49 + -22x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 -49 + -22x + -1x2 = 0 + x2 + -1x2 -49 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -49 + -22x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 22x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(49 + 22x + x2)' equal to zero and attempt to solve: Simplifying 49 + 22x + x2 = 0 Solving 49 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + 22x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + 22x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 22x + x2 = 0 + -49 22x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 22x + x2 = -49 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 = -49 + 121 Reorder the terms: 121 + 22x + x2 = -49 + 121 Combine like terms: -49 + 121 = 72 121 + 22x + x2 = 72 Factor a perfect square on the left side: (x + 11)(x + 11) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 11) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 11 = 8.485281374 Simplifying x + 11 = 8.485281374 Reorder the terms: 11 + x = 8.485281374 Solving 11 + x = 8.485281374 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 = 8.485281374 + -11 Combine like terms: 11 + -11 = 0 0 + x = 8.485281374 + -11 x = 8.485281374 + -11 Combine like terms: 8.485281374 + -11 = -2.514718626 x = -2.514718626 Simplifying x = -2.514718626Subproblem 2
x + 11 = -8.485281374 Simplifying x + 11 = -8.485281374 Reorder the terms: 11 + x = -8.485281374 Solving 11 + x = -8.485281374 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 = -8.485281374 + -11 Combine like terms: 11 + -11 = 0 0 + x = -8.485281374 + -11 x = -8.485281374 + -11 Combine like terms: -8.485281374 + -11 = -19.485281374 x = -19.485281374 Simplifying x = -19.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.514718626, -19.485281374}Solution
x = {-2.514718626, -19.485281374}
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