find the value of t in the following quadratic equation-
4.9t^2 - 2t - 1 = 0
Answers
Answer:
Step-by-step explanation:Simplifying
4.9t2 + 2t + -1 = 0
Reorder the terms:
-1 + 2t + 4.9t2 = 0
Solving
-1 + 2t + 4.9t2 = 0
Solving for variable 't'.
Begin completing the square. Divide all terms by
4.9 the coefficient of the squared term:
Divide each side by '4.9'.
-0.2040816327 + 0.4081632653t + t2 = 0
Move the constant term to the right:
Add '0.2040816327' to each side of the equation.
-0.2040816327 + 0.4081632653t + 0.2040816327 + t2 = 0 + 0.2040816327
Reorder the terms:
-0.2040816327 + 0.2040816327 + 0.4081632653t + t2 = 0 + 0.2040816327
Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + 0.4081632653t + t2 = 0 + 0.2040816327
0.4081632653t + t2 = 0 + 0.2040816327
Combine like terms: 0 + 0.2040816327 = 0.2040816327
0.4081632653t + t2 = 0.2040816327
The t term is 0.4081632653t. Take half its coefficient (0.2040816327).
Square it (0.04164931281) and add it to both sides.
Add '0.04164931281' to each side of the equation.
0.4081632653t + 0.04164931281 + t2 = 0.2040816327 + 0.04164931281
Reorder the terms:
0.04164931281 + 0.4081632653t + t2 = 0.2040816327 + 0.04164931281
Combine like terms: 0.2040816327 + 0.04164931281 = 0.24573094551
0.04164931281 + 0.4081632653t + t2 = 0.24573094551
Factor a perfect square on the left side:
(t + 0.2040816327)(t + 0.2040816327) = 0.24573094551
Calculate the square root of the right side: 0.495712563
Break this problem into two subproblems by setting
(t + 0.2040816327) equal to 0.495712563 and -0.495712563.
hope this helped!