4.9t^2+15t+1.9=0

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Solution for 4.9t^2+15t+1.9=0 equation:


Simplifying
4.9t2 + 15t + 1.9 = 0

Reorder the terms:
1.9 + 15t + 4.9t2 = 0

Solving
1.9 + 15t + 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'.
0.387755102 + 3.06122449t + t2 = 0

Move the constant term to the right:

Add '-0.387755102' to each side of the equation.
0.387755102 + 3.06122449t + -0.387755102 + t2 = 0 + -0.387755102

Reorder the terms:
0.387755102 + -0.387755102 + 3.06122449t + t2 = 0 + -0.387755102

Combine like terms: 0.387755102 + -0.387755102 = 0.000000000
0.000000000 + 3.06122449t + t2 = 0 + -0.387755102
3.06122449t + t2 = 0 + -0.387755102

Combine like terms: 0 + -0.387755102 = -0.387755102
3.06122449t + t2 = -0.387755102

The t term is 3.06122449t.  Take half its coefficient (1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
3.06122449t + 2.342773845 + t2 = -0.387755102 + 2.342773845

Reorder the terms:
2.342773845 + 3.06122449t + t2 = -0.387755102 + 2.342773845

Combine like terms: -0.387755102 + 2.342773845 = 1.955018743
2.342773845 + 3.06122449t + t2 = 1.955018743

Factor a perfect square on the left side:
(t + 1.530612245)(t + 1.530612245) = 1.955018743

Calculate the square root of the right side: 1.398219848

Break this problem into two subproblems by setting 
(t + 1.530612245) equal to 1.398219848 and -1.398219848.

Subproblem 1

t + 1.530612245 = 1.398219848 Simplifying t + 1.530612245 = 1.398219848 Reorder the terms: 1.530612245 + t = 1.398219848 Solving 1.530612245 + t = 1.398219848 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = 1.398219848 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 1.398219848 + -1.530612245 t = 1.398219848 + -1.530612245 Combine like terms: 1.398219848 + -1.530612245 = -0.132392397 t = -0.132392397 Simplifying t = -0.132392397

Subproblem 2

t + 1.530612245 = -1.398219848 Simplifying t + 1.530612245 = -1.398219848 Reorder the terms: 1.530612245 + t = -1.398219848 Solving 1.530612245 + t = -1.398219848 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = -1.398219848 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -1.398219848 + -1.530612245 t = -1.398219848 + -1.530612245 Combine like terms: -1.398219848 + -1.530612245 = -2.928832093 t = -2.928832093 Simplifying t = -2.928832093

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.132392397, -2.928832093}

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