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Simplifying x(x + 1) + (x + 2) = 180 Reorder the terms: x(1 + x) + (x + 2) = 180 (1 * x + x * x) + (x + 2) = 180 (1x + x2) + (x + 2) = 180 Reorder the terms: 1x + x2 + (2 + x) = 180 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 180 Reorder the terms: 2 + 1x + x + x2 = 180 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 180 Solving 2 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + 2x + x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + 2x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 2x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 2x + x2 = 0 + 178 2x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 2x + x2 = 178 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 178 + 1 Reorder the terms: 1 + 2x + x2 = 178 + 1 Combine like terms: 178 + 1 = 179 1 + 2x + x2 = 179 Factor a perfect square on the left side: (x + 1)(x + 1) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (x + 1) equal to 13.37908816 and -13.37908816.Subproblem 1
x + 1 = 13.37908816 Simplifying x + 1 = 13.37908816 Reorder the terms: 1 + x = 13.37908816 Solving 1 + x = 13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.37908816 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.37908816 + -1 x = 13.37908816 + -1 Combine like terms: 13.37908816 + -1 = 12.37908816 x = 12.37908816 Simplifying x = 12.37908816Subproblem 2
x + 1 = -13.37908816 Simplifying x + 1 = -13.37908816 Reorder the terms: 1 + x = -13.37908816 Solving 1 + x = -13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.37908816 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.37908816 + -1 x = -13.37908816 + -1 Combine like terms: -13.37908816 + -1 = -14.37908816 x = -14.37908816 Simplifying x = -14.37908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.37908816, -14.37908816}
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