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Simplifying (x + 7) + (x2 + 9x + 19) = 180 Reorder the terms: (7 + x) + (x2 + 9x + 19) = 180 Remove parenthesis around (7 + x) 7 + x + (x2 + 9x + 19) = 180 Reorder the terms: 7 + x + (19 + 9x + x2) = 180 Remove parenthesis around (19 + 9x + x2) 7 + x + 19 + 9x + x2 = 180 Reorder the terms: 7 + 19 + x + 9x + x2 = 180 Combine like terms: 7 + 19 = 26 26 + x + 9x + x2 = 180 Combine like terms: x + 9x = 10x 26 + 10x + x2 = 180 Solving 26 + 10x + x2 = 180 Solving for variable 'x'. Reorder the terms: 26 + -180 + 10x + x2 = 180 + -180 Combine like terms: 26 + -180 = -154 -154 + 10x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -154 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 10x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 10x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 10x + x2 = 0 + 154 10x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 10x + x2 = 154 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 154 + 25 Reorder the terms: 25 + 10x + x2 = 154 + 25 Combine like terms: 154 + 25 = 179 25 + 10x + x2 = 179 Factor a perfect square on the left side: (x + 5)(x + 5) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (x + 5) equal to 13.37908816 and -13.37908816.Subproblem 1
x + 5 = 13.37908816 Simplifying x + 5 = 13.37908816 Reorder the terms: 5 + x = 13.37908816 Solving 5 + x = 13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 13.37908816 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.37908816 + -5 x = 13.37908816 + -5 Combine like terms: 13.37908816 + -5 = 8.37908816 x = 8.37908816 Simplifying x = 8.37908816Subproblem 2
x + 5 = -13.37908816 Simplifying x + 5 = -13.37908816 Reorder the terms: 5 + x = -13.37908816 Solving 5 + x = -13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -13.37908816 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.37908816 + -5 x = -13.37908816 + -5 Combine like terms: -13.37908816 + -5 = -18.37908816 x = -18.37908816 Simplifying x = -18.37908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.37908816, -18.37908816}
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