Cannot virtualize 64bit vagrant boxes

I run Ubuntu 14.04. My CPU is Intel Core 2 Duo CPU P7450. It supports neither VT-x nor EPT. But it is 64bit.

I can only virtualize 32bit boxes with success. When I try 64bit i get a never-ending

default: Warning: Connection timeout. Retrying...

Tried to start the VM from GUI, and I took only this clue:

I pressed "Continue" and nothing happened but a black empty screen. Any solution? Why cannot I run 64bit VMs with a 64bit CPU???

The reason we can not run a 64-bit guest in Virtual Box even when run on a 64-bit host is that 64-bit guests don't make use of software virtualization. They depend on hardware virtualization to work:

VirtualBox's 64-bit guest support (added with version 2.0) and multiprocessing (SMP, added with version 3.0) both require hardware virtualization to be enabled.^{Virtual Box Manual}

In case our CPU supports it we need to enable it in the BIOS of our computer:

• How do I enable hardware virtualization technology (VT-x) for use in Virtualbox?

In case our CPU does not support hardware virtualization we are unable to run 64-bit guests. We will still be able to install and run 32-bit guests.