Question

5.( x+4).(x-4)+76=(2x-1).(x-4)+(3x-1).(x+4)

Answer 1

\(\left(x+4\right)\left(x-4\right)+76=\left(2x-1\right)\left(x-4\right)+\left(3x-1\right)\left(x+4\right)\\ \Leftrightarrow x^2-16+76=2x^2-x-8x+4+3x^2-x+12x-4\\ \Leftrightarrow x^2+60=5x^2+2x\\ \Leftrightarrow-4x^2-2x+60=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1+\sqrt{241}}{4}\\x=\dfrac{-1-\sqrt{241}}{4}\end{matrix}\right.\)

Answer 2

\(5.\left(x+4\right)\left(x-4\right)+76=\left(2x-1\right)\left(x-4\right)+\left(3x-1\right)\left(x+4\right)\\ \Leftrightarrow5\left(x^2-16\right)+76=2x^2-x-8x+4+3x^2-x+12x-4\\ \Leftrightarrow5x^2-80+76=5x^2+2x\\ \Leftrightarrow\left(5x^2-5x^2\right)-2x+\left(-80+76\right)=0\\ \Leftrightarrow-2x-4=0\\ \Leftrightarrow-2x=4\\ \Leftrightarrow x=-2\)