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Simplifying (x + 10) + x(x + 5) = 180 Reorder the terms: (10 + x) + x(x + 5) = 180 Remove parenthesis around (10 + x) 10 + x + x(x + 5) = 180 Reorder the terms: 10 + x + x(5 + x) = 180 10 + x + (5 * x + x * x) = 180 10 + x + (5x + x2) = 180 Combine like terms: x + 5x = 6x 10 + 6x + x2 = 180 Solving 10 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 10 + -180 + 6x + x2 = 180 + -180 Combine like terms: 10 + -180 = -170 -170 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -170 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 6x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 6x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 6x + x2 = 0 + 170 6x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 6x + x2 = 170 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 170 + 9 Reorder the terms: 9 + 6x + x2 = 170 + 9 Combine like terms: 170 + 9 = 179 9 + 6x + x2 = 179 Factor a perfect square on the left side: (x + 3)(x + 3) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (x + 3) equal to 13.37908816 and -13.37908816.Subproblem 1
x + 3 = 13.37908816 Simplifying x + 3 = 13.37908816 Reorder the terms: 3 + x = 13.37908816 Solving 3 + x = 13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.37908816 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.37908816 + -3 x = 13.37908816 + -3 Combine like terms: 13.37908816 + -3 = 10.37908816 x = 10.37908816 Simplifying x = 10.37908816Subproblem 2
x + 3 = -13.37908816 Simplifying x + 3 = -13.37908816 Reorder the terms: 3 + x = -13.37908816 Solving 3 + x = -13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.37908816 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.37908816 + -3 x = -13.37908816 + -3 Combine like terms: -13.37908816 + -3 = -16.37908816 x = -16.37908816 Simplifying x = -16.37908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.37908816, -16.37908816}
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