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Answer :
The equation x^2−10x+27=0, that would be 25. So, the correct step in completing the square is x^2−10x+25=−27+25.
The equation Thomas solves by completing the square is x2−10x+27=0. Completing the square requires adding and subtracting the square of half the coefficient of x (which is (−10)/2=−5).
The square of −5 is 25.
Therefore, one of the potential steps Thomas took should involve adding 25 to both sides of the equation.
Here, the correct step is x2−10x+25=−27+25.
It is essentially changing the original equation to (x-5)2=−2. x2−10x+100=−27+100 or x2−10x+100=−27 are not correct steps as they involve adding 100 which is incorrectly derived from the original equation.
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