4.9t^2+3.38t-0.58=0

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Solution for 4.9t^2+3.38t-0.58=0 equation:


Simplifying
4.9t2 + 3.38t + -0.58 = 0

Reorder the terms:
-0.58 + 3.38t + 4.9t2 = 0

Solving
-0.58 + 3.38t + 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'.
-0.1183673469 + 0.6897959184t + t2 = 0

Move the constant term to the right:

Add '0.1183673469' to each side of the equation.
-0.1183673469 + 0.6897959184t + 0.1183673469 + t2 = 0 + 0.1183673469

Reorder the terms:
-0.1183673469 + 0.1183673469 + 0.6897959184t + t2 = 0 + 0.1183673469

Combine like terms: -0.1183673469 + 0.1183673469 = 0.0000000000
0.0000000000 + 0.6897959184t + t2 = 0 + 0.1183673469
0.6897959184t + t2 = 0 + 0.1183673469

Combine like terms: 0 + 0.1183673469 = 0.1183673469
0.6897959184t + t2 = 0.1183673469

The t term is 0.6897959184t.  Take half its coefficient (0.3448979592).
Square it (0.1189546023) and add it to both sides.

Add '0.1189546023' to each side of the equation.
0.6897959184t + 0.1189546023 + t2 = 0.1183673469 + 0.1189546023

Reorder the terms:
0.1189546023 + 0.6897959184t + t2 = 0.1183673469 + 0.1189546023

Combine like terms: 0.1183673469 + 0.1189546023 = 0.2373219492
0.1189546023 + 0.6897959184t + t2 = 0.2373219492

Factor a perfect square on the left side:
(t + 0.3448979592)(t + 0.3448979592) = 0.2373219492

Calculate the square root of the right side: 0.487157007

Break this problem into two subproblems by setting 
(t + 0.3448979592) equal to 0.487157007 and -0.487157007.

Subproblem 1

t + 0.3448979592 = 0.487157007 Simplifying t + 0.3448979592 = 0.487157007 Reorder the terms: 0.3448979592 + t = 0.487157007 Solving 0.3448979592 + t = 0.487157007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3448979592' to each side of the equation. 0.3448979592 + -0.3448979592 + t = 0.487157007 + -0.3448979592 Combine like terms: 0.3448979592 + -0.3448979592 = 0.0000000000 0.0000000000 + t = 0.487157007 + -0.3448979592 t = 0.487157007 + -0.3448979592 Combine like terms: 0.487157007 + -0.3448979592 = 0.1422590478 t = 0.1422590478 Simplifying t = 0.1422590478

Subproblem 2

t + 0.3448979592 = -0.487157007 Simplifying t + 0.3448979592 = -0.487157007 Reorder the terms: 0.3448979592 + t = -0.487157007 Solving 0.3448979592 + t = -0.487157007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3448979592' to each side of the equation. 0.3448979592 + -0.3448979592 + t = -0.487157007 + -0.3448979592 Combine like terms: 0.3448979592 + -0.3448979592 = 0.0000000000 0.0000000000 + t = -0.487157007 + -0.3448979592 t = -0.487157007 + -0.3448979592 Combine like terms: -0.487157007 + -0.3448979592 = -0.8320549662 t = -0.8320549662 Simplifying t = -0.8320549662

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.1422590478, -0.8320549662}

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