Thank you, please leave calculations so I can check your method, thank you.

This is just completing the square. First factor out a –1 ...
–1(t² – 20t + ____) + _____
Take half the middle coeficient and sqaure it. (–20/2)² = 10² = 100. Put it in the first blank:
–1(t² – 20t + 100) + ___?__ Now what do you need in the second blank to balance it?
By adding +100 insiode the parentheses that is multiplied by a –1, you have really subtracted 100, so you need to add 100 to keep the expression equal to its original value...
–1(t² – 20t + 100) + 100 Now recocognize the perfect sqaure ...
–(t – 10)² + 100 or in the form you specified: 100 – (t – 10)²
–1(t² – 20t + ____) + _____
Take half the middle coeficient and sqaure it. (–20/2)² = 10² = 100. Put it in the first blank:
–1(t² – 20t + 100) + ___?__ Now what do you need in the second blank to balance it?
By adding +100 insiode the parentheses that is multiplied by a –1, you have really subtracted 100, so you need to add 100 to keep the expression equal to its original value...
–1(t² – 20t + 100) + 100 Now recocognize the perfect sqaure ...
–(t – 10)² + 100 or in the form you specified: 100 – (t – 10)²

p t^2 +2qt q^2 = 20t t^2
so, q =10, q^2 =100, hence p =100 ...so,
100 (t10)^2
so, q =10, q^2 =100, hence p =100 ...so,
100 (t10)^2