Calculate 5619

Jana had to calculate 70 tasks, and if she had solved two more daily tasks than she had planned, she would have finished four days earlier. How many days did she have to calculate the tasks?

Correct answer:

d =  14

Step-by-step explanation:

$$\begin{gathered} d\cdot v=70 \\ (d-4)\cdot (v+2)=70 \\ (d-4)\cdot (70/d+2)=70 \\ (d-4)\cdot (70+2d)=70d \\ (d-4)\cdot (70+2d)=70d \\ 2d^2-8d-280=0 \\ 2...\text{ prime number} \\ 8=2^3 \\ 280=2^3\cdot 5\cdot 7 \\ \text{GCD}(2,8,280)=2 \\ {d}^2-4d-140=0 \\ a=1;b=-4;c=-140 \\ D=b^2-4ac=4^2-4\cdot 1\cdot (-140)=576 \\ D>0 \\ {d}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{4\pm \sqrt{576}}{2} \\ {d}_{1,2}=\frac{4\pm 24}{2} \\ {d}_{1,2}=2\pm 12 \\ {d}_1=14 \\ {d}_2=-10 \\ d>0 \\ d=d_1=14 \end{gathered}$$

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