Quicktest

SupportAssist did not exist when the L702x was produced. SupportAssist wasn't designed to support models that existed before it was released, so I wouldn't trust its results.

Dell Diagnostics

If you want to test your hardware, run Dell Diagnostics:
Immediately after pressing the power button to turn on the laptop (or after clicking the Reboot command), press and hold F12 to enter the One Time Boot Menu, select Diagnostics and press Enter. The Dell Diagnostics will test all your hardware. Select the longer, more complete test (I forget the exact wording).

memtest86+

If you suspect memory issues, use a more thorough testing utility such as memtest86+.

memtest86+ runs from a bootable flash drive or CD/DVD, so it can test more of the memory than is possible with Windows Memory Diagnostic. memtest86+ should be allowed to run for at least three passes, which on older hardware can take many hours. Over at TenForums they say that for solid test results you should let it run at least 8 passes in a single session. On your L702x, that could take a couple of days. 
https://www.tenforums.com/tutorials/14201-memtest86-test-ram.html

Any error reported by memtest86+ means that there is a hardware problem, though not necessarily in the RAM. Errors could relate to issues with CPU, motherboard, RAM slots, etc. There is a process to follow to test RAM sticks individually in each slot, etc., to gradually narrow down the source of the errors.

While it's running, make note of the CPU temperature, to see if it's getting high. If it is, shut down the test and do some physical maintenance.

Physical maintenance

You didn't say why you ran that test. Is the laptop having issues? As it's 11 years old, then the thermal compound has dried out and cannot adequately transfer heat away from the processor, and there may be a lot of dust inside the laptop and maybe inside the fan and heat fins. So, your laptop is unable to adequately cool itself.

You might consider an internal cleaning. Open it up to clean out dust. Disassemble the fan to clean out dust and fluff. I found a fair bit in two laptops I worked on recently. Remove the heat sink, remove the old thermal compound and apply new thermal compound before reinstalling the heat sink.

While you're in there, replace the CMOS battery. If it isn't dead, it soon will be. BIOS settings and date/time can't be saved without a functioning CMOS battery.

Follow the disassembly and reassembly steps in Dell's Service Manual.
Look on YouTube for videos showing disassembly of your model. But, be cautious with them, as some use steps or methods that are not appropriate. Use the videos to add to your understanding of what to do, but follow the steps in Dell's manual.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard.

I have essentially the same model, L502x, which is the 15" version of what you have. I opened mine to do that work that I just described. If you have questions, ask.