Question 177874
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Somewhere in the process of applying the distributive property and collecting like terms you went astray.


*[tex \Large 4x(x-2)-5x(x-1)=2]


*[tex \Large 4x^2 - 8x - 5x^2 + 5x = 2]


*[tex \Large -x^2 - 3x - 2 = 0]


*[tex \Large x^2 + 3x + 2 = 0] (after multiplying by -1)


Which factors quite tidily:


*[tex \Large (x + 1)(x + 2) = 0]


Hence, *[tex \Large x = -1 \text {   or   } \math x = -2]


And the following graph of the original function verifies the calculations.

{{{drawing(
600, 600, -5, 5, -5, 5,
grid(1),
graph(
600, 600, -5, 5, -5, 5,
y=4x^2 - 8x - 5x^2 + 5x - 2
))}}}

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