4.9t^2+100t+50=0

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Solution for 4.9t^2+100t+50=0 equation:


Simplifying
4.9t2 + 100t + 50 = 0

Reorder the terms:
50 + 100t + 4.9t2 = 0

Solving
50 + 100t + 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'.
10.20408163 + 20.40816327t + t2 = 0

Move the constant term to the right:

Add '-10.20408163' to each side of the equation.
10.20408163 + 20.40816327t + -10.20408163 + t2 = 0 + -10.20408163

Reorder the terms:
10.20408163 + -10.20408163 + 20.40816327t + t2 = 0 + -10.20408163

Combine like terms: 10.20408163 + -10.20408163 = 0.00000000
0.00000000 + 20.40816327t + t2 = 0 + -10.20408163
20.40816327t + t2 = 0 + -10.20408163

Combine like terms: 0 + -10.20408163 = -10.20408163
20.40816327t + t2 = -10.20408163

The t term is 20.40816327t.  Take half its coefficient (10.20408164).
Square it (104.1232821) and add it to both sides.

Add '104.1232821' to each side of the equation.
20.40816327t + 104.1232821 + t2 = -10.20408163 + 104.1232821

Reorder the terms:
104.1232821 + 20.40816327t + t2 = -10.20408163 + 104.1232821

Combine like terms: -10.20408163 + 104.1232821 = 93.91920047
104.1232821 + 20.40816327t + t2 = 93.91920047

Factor a perfect square on the left side:
(t + 10.20408164)(t + 10.20408164) = 93.91920047

Calculate the square root of the right side: 9.691191901

Break this problem into two subproblems by setting 
(t + 10.20408164) equal to 9.691191901 and -9.691191901.

Subproblem 1

t + 10.20408164 = 9.691191901 Simplifying t + 10.20408164 = 9.691191901 Reorder the terms: 10.20408164 + t = 9.691191901 Solving 10.20408164 + t = 9.691191901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.20408164' to each side of the equation. 10.20408164 + -10.20408164 + t = 9.691191901 + -10.20408164 Combine like terms: 10.20408164 + -10.20408164 = 0.00000000 0.00000000 + t = 9.691191901 + -10.20408164 t = 9.691191901 + -10.20408164 Combine like terms: 9.691191901 + -10.20408164 = -0.512889739 t = -0.512889739 Simplifying t = -0.512889739

Subproblem 2

t + 10.20408164 = -9.691191901 Simplifying t + 10.20408164 = -9.691191901 Reorder the terms: 10.20408164 + t = -9.691191901 Solving 10.20408164 + t = -9.691191901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.20408164' to each side of the equation. 10.20408164 + -10.20408164 + t = -9.691191901 + -10.20408164 Combine like terms: 10.20408164 + -10.20408164 = 0.00000000 0.00000000 + t = -9.691191901 + -10.20408164 t = -9.691191901 + -10.20408164 Combine like terms: -9.691191901 + -10.20408164 = -19.895273541 t = -19.895273541 Simplifying t = -19.895273541

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.512889739, -19.895273541}

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