Question 888096
Set the expression equal to zero. Factor and solve.


x^4 - x^3 - 4x^2 + 4 = 0


(x^4 - x^3) + (-4x^2 + 4) = 0


x^3(x - 1) + (-4x^2 + 4) = 0


x^3(x - 1) -4(x^2 - 1) = 0


x^3(x - 1) -4(x - 1)(x + 1) = 0


x^3(x - 1) -4(x + 1)(x - 1) = 0


(x^3 - 4(x+1))(x - 1) = 0


Then you use the zero product property to get these two equations


x^3 - 4(x+1) = 0 or x-1=0


The first equation x^3 - 4(x+1) = 0 needs a calculator because this is a cubic (most cubics are nearly impossible to solve by hand)


The approximate solution to x^3 - 4(x+1)=0 is x = 2.382975768


The solution to x-1 = 0 is x = 1


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So the two real number solutions are


x = 1 or x = 2.382975768