-4.9t^2-14t+30=0

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Solution for -4.9t^2-14t+30=0 equation:


Simplifying
-4.9t2 + -14t + 30 = 0

Reorder the terms:
30 + -14t + -4.9t2 = 0

Solving
30 + -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'.
-6.12244898 + 2.857142857t + t2 = 0

Move the constant term to the right:

Add '6.12244898' to each side of the equation.
-6.12244898 + 2.857142857t + 6.12244898 + t2 = 0 + 6.12244898

Reorder the terms:
-6.12244898 + 6.12244898 + 2.857142857t + t2 = 0 + 6.12244898

Combine like terms: -6.12244898 + 6.12244898 = 0.00000000
0.00000000 + 2.857142857t + t2 = 0 + 6.12244898
2.857142857t + t2 = 0 + 6.12244898

Combine like terms: 0 + 6.12244898 = 6.12244898
2.857142857t + t2 = 6.12244898

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 = 6.12244898 + 2.040816328

Reorder the terms:
2.040816328 + 2.857142857t + t2 = 6.12244898 + 2.040816328

Combine like terms: 6.12244898 + 2.040816328 = 8.163265308
2.040816328 + 2.857142857t + t2 = 8.163265308

Factor a perfect square on the left side:
(t + 1.428571429)(t + 1.428571429) = 8.163265308

Calculate the square root of the right side: 2.857142857

Break this problem into two subproblems by setting 
(t + 1.428571429) equal to 2.857142857 and -2.857142857.

Subproblem 1

t + 1.428571429 = 2.857142857 Simplifying t + 1.428571429 = 2.857142857 Reorder the terms: 1.428571429 + t = 2.857142857 Solving 1.428571429 + t = 2.857142857 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 = 2.857142857 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + t = 2.857142857 + -1.428571429 t = 2.857142857 + -1.428571429 Combine like terms: 2.857142857 + -1.428571429 = 1.428571428 t = 1.428571428 Simplifying t = 1.428571428

Subproblem 2

t + 1.428571429 = -2.857142857 Simplifying t + 1.428571429 = -2.857142857 Reorder the terms: 1.428571429 + t = -2.857142857 Solving 1.428571429 + t = -2.857142857 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 = -2.857142857 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + t = -2.857142857 + -1.428571429 t = -2.857142857 + -1.428571429 Combine like terms: -2.857142857 + -1.428571429 = -4.285714286 t = -4.285714286 Simplifying t = -4.285714286

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.428571428, -4.285714286}

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