4.9t^2-14t-2=0

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Solution for 4.9t^2-14t-2=0 equation:


Simplifying
4.9t2 + -14t + -2 = 0

Reorder the terms:
-2 + -14t + 4.9t2 = 0

Solving
-2 + -14t + 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 + -2.857142857t + t2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -2.857142857t + 0.4081632653 + t2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -2.857142857t + t2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -2.857142857t + t2 = 0 + 0.4081632653
-2.857142857t + t2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-2.857142857t + t2 = 0.4081632653

The t term is -2.857142857t.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857t + 2.040816328 + t2 = 0.4081632653 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857t + t2 = 0.4081632653 + 2.040816328

Combine like terms: 0.4081632653 + 2.040816328 = 2.4489795933
2.040816328 + -2.857142857t + t2 = 2.4489795933

Factor a perfect square on the left side:
(t + -1.428571429)(t + -1.428571429) = 2.4489795933

Calculate the square root of the right side: 1.564921593

Break this problem into two subproblems by setting 
(t + -1.428571429) equal to 1.564921593 and -1.564921593.

Subproblem 1

t + -1.428571429 = 1.564921593 Simplifying t + -1.428571429 = 1.564921593 Reorder the terms: -1.428571429 + t = 1.564921593 Solving -1.428571429 + t = 1.564921593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 1.564921593 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.564921593 + 1.428571429 t = 1.564921593 + 1.428571429 Combine like terms: 1.564921593 + 1.428571429 = 2.993493022 t = 2.993493022 Simplifying t = 2.993493022

Subproblem 2

t + -1.428571429 = -1.564921593 Simplifying t + -1.428571429 = -1.564921593 Reorder the terms: -1.428571429 + t = -1.564921593 Solving -1.428571429 + t = -1.564921593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -1.564921593 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.564921593 + 1.428571429 t = -1.564921593 + 1.428571429 Combine like terms: -1.564921593 + 1.428571429 = -0.136350164 t = -0.136350164 Simplifying t = -0.136350164

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.993493022, -0.136350164}

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