The correct step Thomas should have taken when using the completing the square method is x² − 10x + 25= -27 + 25
The standard form of a quadratic equation is given by:
ax² + bx + c = 0
There a is the coefficient of x², b is the coefficient of x and c is a constant.
The solution to the quadratic equation has to solutions.
Given the equation:
x² − 10x + 27 = 0
Solving using completing the square; first subtract 27 from both sides:
x² − 10x + 27 - 27 = 0 - 27
x² − 10x = -27
Add to both sides, the square of half of the coefficient of x (i.e. (-5)² = 25)
x² − 10x + 25= -27 + 25
(x - 5)² = -2
Therefore option C is the correct step, Thomas should have taken to complete the square
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