Let's first simplify the expression step by step:
(x-2)₂ - 5(x² - 9) + 4(x² + 3x - 4)
x - 2 - 5x² + 45 + 4x² + 12x - 16 = 1
-5x² + 4x² + x + 12x - 2 - 16 + 45 = 1
-x + 13x + 27 = 1
12x + 27 = 1
12x = -26
x = -26/12x = -13/6
Therefore, the solution to the equation (x-2)₂-5(x-3)(x+3)+4(x-1)(x+4) = 1 is x = -13/6.
Let's first simplify the expression step by step:
Apply the distributive property to expand the terms:(x-2)₂ - 5(x² - 9) + 4(x² + 3x - 4)
Simplify the expression further:x - 2 - 5x² + 45 + 4x² + 12x - 16 = 1
Combine like terms:-5x² + 4x² + x + 12x - 2 - 16 + 45 = 1
-x + 13x + 27 = 1
12x + 27 = 1
Subtract 27 from both sides:12x = -26
Divide by 12:x = -26/12
x = -13/6
Therefore, the solution to the equation (x-2)₂-5(x-3)(x+3)+4(x-1)(x+4) = 1 is x = -13/6.