Automaker

The automaker now produces daily 4 new cars more than last year, so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles were needed in the previous year?

Correct answer:

x =  10

Step-by-step explanation:

$$\begin{gathered} 360=d\cdot x \\ 360=(d+4)\cdot (x-1) \\ d=4x-4 \\ x(4x-4)=360 \\ 4x^2-4x-360=0 \\ 4=2^2 \\ 360=2^3\cdot 3^2\cdot 5 \\ \text{GCD}(4,4,360)=2^2=4 \\ {x}^2-x-90=0 \\ a=1;b=-1;c=-90 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-90)=361 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1\pm \sqrt{361}}{2} \\ {x}_{1,2}=\frac{1\pm 19}{2} \\ {x}_{1,2}=0.5\pm 9.5 \\ {x}_1=10 \\ {x}_2=-9 \\ \text{ Factored form of the equation: } \\ (x-10)(x+9)=0 \\ x>0 \\ x=10 \\ d=4x-4=410-4=36 \end{gathered}$$

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