5t^2-20t-100=0 how to slove
Answers
This Question is solve by hand.
please make this answer as brainest.
Answer:
Simplifying
5t2 + 20t = 100
Reorder the terms:
20t + 5t2 = 100
Solving
20t + 5t2 = 100
Solving for variable 't'.
Reorder the terms:
-100 + 20t + 5t2 = 100 + -100
Combine like terms: 100 + -100 = 0
-100 + 20t + 5t2 = 0
Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + 4t + t2) = 0
Ignore the factor 5.
Subproblem 1
Set the factor '(-20 + 4t + t2)' equal to zero and attempt to solve:
Simplifying
-20 + 4t + t2 = 0
Solving
-20 + 4t + t2 = 0
Begin completing the square.
Move the constant term to the right:
Add '20' to each side of the equation.
-20 + 4t + 20 + t2 = 0 + 20
Reorder the terms:
-20 + 20 + 4t + t2 = 0 + 20
Combine like terms: -20 + 20 = 0
0 + 4t + t2 = 0 + 20
4t + t2 = 0 + 20
Combine like terms: 0 + 20 = 20
4t + t2 = 20
The t term is 4t. Take half its coefficient (2).
Square it (4) and add it to both sides.
Add '4' to each side of the equation.
4t + 4 + t2 = 20 + 4
Reorder the terms:
4 + 4t + t2 = 20 + 4
Combine like terms: 20 + 4 = 24
4 + 4t + t2 = 24
Factor a perfect square on the left side:
(t + 2)(t + 2) = 24
Calculate the square root of the right side: 4.898979486
Break this problem into two subproblems by setting
(t + 2) equal to 4.898979486 and -4.898979486.