Problem passing parameter in form | Laravel

I have an application for project management, and that each project has its tasks. These tasks can be deleted or completed.

Each task is displayed through a foreach, which is inside a view, being displayed inside a card, and inside this card, has two buttons, one for each action.

To load this page, it is called through a controller (ProjectController) and when clicking the buttons, I call a modal to confirm such completion or deletion and when I confirm, I call the controller (TaskController).

However, when I do any of the actions, I get the same error: Undefined variable: task_id (View: C:\Users\User\project-manager\resources\views\modals\modals.blade.php) (View: C:\Users\User\project-manager\resources\views\modals\modals.blade.php)

ProjectController (displays page with tasks):

public function show($id)
{
    $task = Task::all()
        ->where('project_id', '=', $id);

    $task_id = Task::all()
        ->where('project_id', '=', $id)
        ->first();

    $task_count = count($task);
    $t = $task->where('final_date', '!=', null);
    $task_done = count($t);
    $task_not_done = $task_count - $task_done;
    return view('project.edit', ['project' => Project::findOrFail($id)])
        ->with('task', $task)
        ->with('task_count', $task_count)
        ->with('task_done', $task_done)
        ->with('task_not_done', $task_not_done)
        ->with('task_id', $task_id);
}

Modal for completion / exclusion of tasks:

<!-- Modal to check a task -->
<div class="modal fade" id="check" tabindex="-1" role="dialog" aria-labelledby="exampleModalLabel" aria-hidden="true">
    <div class="modal-dialog modal-sm" role="document">
        <div class="modal-content">
            <div class="modal-header">
                <h4 class="modal-title" id="exampleModalLabel">Atenção!</h4>
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                    <span aria-hidden="true">&times;</span>
                </button>
            </div>
            <div class="modal-body">
                <form action="{{ route('tasks_update', $task_id->id) }}" method="PUT">
                    <p>
                        Você deseja concluir esta tarefa?
                    </p>
                    @csrf
                    <input name="code" id="code" type="hidden" value="1">
                    <div class="modal-footer">
                        <button type="button" class="btn btn-secondary" data-dismiss="modal">Sair</button>
                        <button type="submit" class="btn btn-success">Concluir</button>
                    </div>
                </form>
            </div>
        </div>
    </div>
</div>

Route: Route::put('tasks/{id}', 'TaskController@update')->name('tasks_update');

TaskController (perform update):

public function update(Request $request, $id)
{
    if($request->input('code') == 1){
        DB::table('tasks')
            ->where('id', '=', $id)
            ->update(['check' => 1]);
        return view()->route('projects.show');
    }

    if($request->input('code') == 2) {
        DB::table('tasks')
            ->where('id', '=', $id)
            ->update(['deleted_at' => now()]);
        return view()->route('projects.show');
    }
}

Note: I'm using Laravel's route resourcer; I already tried to leave the modal on the same page where the task cards are being displayed; I also noticed that clicking the button, I can not even get to the controller;