## Task B-3.3.

Solve the equation $x^{2}-x-\sin (\pi x)=-1.25$.
## Second Solution.

As in the first solution, write the equation $x^{2}-x-\sin (\pi x)=-1.25$ in the form $x^{2}-x+1.25=\sin (\pi x)$.

Let $f(x)=x^{2}-x+1.25$ and $g(x)=\sin (\pi x)$.

We solve this graphically. We draw the graphs of functions $f$ and $g$ in the same coordinate system.

![](https://cdn.mathpix.com/cropped/2024_05_30_6dc7744662d888032875g-19.jpg?height=674&width=925&top_left_y=574&top_left_x=491)

The graph of the quadratic function $f$ is a parabola with its vertex at point $B(0.5,1)$. This means that the minimum value of function $f$ is 1, and it is achieved only for $x=0.5$.

On the other hand, the amplitude of function $g$ is 1, so the maximum value of function $g$ is 1.

Therefore, the only possibility is that both functions achieve the value 1 for the same $x$. Clearly, there is only one such possibility for $x=0.5$.

Let's check if $g(0.5)=1$.

We have $g(0.5)=\sin (\pi \cdot 0.5)=1$. Therefore, the only solution is $x=0.5$.

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