3t+9.81t^2=4

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Solution for 3t+9.81t^2=4 equation:


Simplifying
3t + 9.81t2 = 4

Solving
3t + 9.81t2 = 4

Solving for variable 't'.

Reorder the terms:
-4 + 3t + 9.81t2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 3t + 9.81t2 = 0

Begin completing the square.  Divide all terms by
9.81 the coefficient of the squared term: 

Divide each side by '9.81'.
-0.4077471967 + 0.3058103976t + t2 = 0

Move the constant term to the right:

Add '0.4077471967' to each side of the equation.
-0.4077471967 + 0.3058103976t + 0.4077471967 + t2 = 0 + 0.4077471967

Reorder the terms:
-0.4077471967 + 0.4077471967 + 0.3058103976t + t2 = 0 + 0.4077471967

Combine like terms: -0.4077471967 + 0.4077471967 = 0.0000000000
0.0000000000 + 0.3058103976t + t2 = 0 + 0.4077471967
0.3058103976t + t2 = 0 + 0.4077471967

Combine like terms: 0 + 0.4077471967 = 0.4077471967
0.3058103976t + t2 = 0.4077471967

The t term is 0.3058103976t.  Take half its coefficient (0.1529051988).
Square it (0.02337999982) and add it to both sides.

Add '0.02337999982' to each side of the equation.
0.3058103976t + 0.02337999982 + t2 = 0.4077471967 + 0.02337999982

Reorder the terms:
0.02337999982 + 0.3058103976t + t2 = 0.4077471967 + 0.02337999982

Combine like terms: 0.4077471967 + 0.02337999982 = 0.43112719652
0.02337999982 + 0.3058103976t + t2 = 0.43112719652

Factor a perfect square on the left side:
(t + 0.1529051988)(t + 0.1529051988) = 0.43112719652

Calculate the square root of the right side: 0.656602769

Break this problem into two subproblems by setting 
(t + 0.1529051988) equal to 0.656602769 and -0.656602769.

Subproblem 1

t + 0.1529051988 = 0.656602769 Simplifying t + 0.1529051988 = 0.656602769 Reorder the terms: 0.1529051988 + t = 0.656602769 Solving 0.1529051988 + t = 0.656602769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1529051988' to each side of the equation. 0.1529051988 + -0.1529051988 + t = 0.656602769 + -0.1529051988 Combine like terms: 0.1529051988 + -0.1529051988 = 0.0000000000 0.0000000000 + t = 0.656602769 + -0.1529051988 t = 0.656602769 + -0.1529051988 Combine like terms: 0.656602769 + -0.1529051988 = 0.5036975702 t = 0.5036975702 Simplifying t = 0.5036975702

Subproblem 2

t + 0.1529051988 = -0.656602769 Simplifying t + 0.1529051988 = -0.656602769 Reorder the terms: 0.1529051988 + t = -0.656602769 Solving 0.1529051988 + t = -0.656602769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1529051988' to each side of the equation. 0.1529051988 + -0.1529051988 + t = -0.656602769 + -0.1529051988 Combine like terms: 0.1529051988 + -0.1529051988 = 0.0000000000 0.0000000000 + t = -0.656602769 + -0.1529051988 t = -0.656602769 + -0.1529051988 Combine like terms: -0.656602769 + -0.1529051988 = -0.8095079678 t = -0.8095079678 Simplifying t = -0.8095079678

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.5036975702, -0.8095079678}

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