The investigator arrived after the road had been cleared, so all she had was a photograph, a tape measure, and the marks the tyres had left on the asphalt.
The driver's claim was that he had been travelling slowly. From the length of the marks she could work backwards and test that.
She set up the arithmetic and it gave her two numbers. This did not surprise her. The step she had used — removing a square root by squaring — always risks handing back an answer that the original situation never allowed.
One of the two numbers was negative. She crossed it out without a second thought. A car cannot leave a mark of negative length, and it cannot travel at a negative speed down a straight road in daylight. The arithmetic did not know that. She did.
Her colleague asked whether crossing out an answer was allowed. She said it was not only allowed, it was required. "Squaring both sides is a step, not a truth. Whatever comes out of it has to be taken back to the beginning and tried against the real thing."
She took the surviving number back to the marks on the road, and it fitted. The other one had never been an answer at all — only a shadow left behind by the method she had used to find it.