4.9t^2+23.5t+2=0

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Solution for 4.9t^2+23.5t+2=0 equation:


Simplifying
4.9t2 + 23.5t + 2 = 0

Reorder the terms:
2 + 23.5t + 4.9t2 = 0

Solving
2 + 23.5t + 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'.
0.4081632653 + 4.795918367t + t2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + 4.795918367t + -0.4081632653 + t2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + 4.795918367t + t2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + 4.795918367t + t2 = 0 + -0.4081632653
4.795918367t + t2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
4.795918367t + t2 = -0.4081632653

The t term is 4.795918367t.  Take half its coefficient (2.397959184).
Square it (5.750208248) and add it to both sides.

Add '5.750208248' to each side of the equation.
4.795918367t + 5.750208248 + t2 = -0.4081632653 + 5.750208248

Reorder the terms:
5.750208248 + 4.795918367t + t2 = -0.4081632653 + 5.750208248

Combine like terms: -0.4081632653 + 5.750208248 = 5.3420449827
5.750208248 + 4.795918367t + t2 = 5.3420449827

Factor a perfect square on the left side:
(t + 2.397959184)(t + 2.397959184) = 5.3420449827

Calculate the square root of the right side: 2.311286435

Break this problem into two subproblems by setting 
(t + 2.397959184) equal to 2.311286435 and -2.311286435.

Subproblem 1

t + 2.397959184 = 2.311286435 Simplifying t + 2.397959184 = 2.311286435 Reorder the terms: 2.397959184 + t = 2.311286435 Solving 2.397959184 + t = 2.311286435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.397959184' to each side of the equation. 2.397959184 + -2.397959184 + t = 2.311286435 + -2.397959184 Combine like terms: 2.397959184 + -2.397959184 = 0.000000000 0.000000000 + t = 2.311286435 + -2.397959184 t = 2.311286435 + -2.397959184 Combine like terms: 2.311286435 + -2.397959184 = -0.086672749 t = -0.086672749 Simplifying t = -0.086672749

Subproblem 2

t + 2.397959184 = -2.311286435 Simplifying t + 2.397959184 = -2.311286435 Reorder the terms: 2.397959184 + t = -2.311286435 Solving 2.397959184 + t = -2.311286435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.397959184' to each side of the equation. 2.397959184 + -2.397959184 + t = -2.311286435 + -2.397959184 Combine like terms: 2.397959184 + -2.397959184 = 0.000000000 0.000000000 + t = -2.311286435 + -2.397959184 t = -2.311286435 + -2.397959184 Combine like terms: -2.311286435 + -2.397959184 = -4.709245619 t = -4.709245619 Simplifying t = -4.709245619

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.086672749, -4.709245619}

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