Answer:
5(x - 4)^2 - 379
Step-by-step explanation:
First, let’s complete the square by finding the value of b:
Divide the coefficient of the linear term (-40x) by 2: (\frac{-40}{2} = -20).
Square this value: ((-20)^2 = 400).
Now, add and subtract this value inside the expression: [5x^2 - 40x + 21 = 5x^2 - 40x + 400 - 400 + 21]
Rearrange the expression: [5x^2 - 40x + 400 - 400 + 21 = 5(x^2 - 8x + 80) - 379]
Finally, we have the expression in the desired form: [5x^2 - 40x + 21 = 5(x - 4)^2 - 379]
Therefore, the expression can be written as 5(x - 4)^2 - 379.
