-4.9t^2+24t-13=0

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Solution for -4.9t^2+24t-13=0 equation: 


Simplifying
-4.9t2 + 24t + -13 = 0

Reorder the terms:
-13 + 24t + -4.9t2 = 0

Solving
-13 + 24t + -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'.
2.653061224 + -4.897959184t + t2 = 0

Move the constant term to the right:

Add '-2.653061224' to each side of the equation.
2.653061224 + -4.897959184t + -2.653061224 + t2 = 0 + -2.653061224

Reorder the terms:
2.653061224 + -2.653061224 + -4.897959184t + t2 = 0 + -2.653061224

Combine like terms: 2.653061224 + -2.653061224 = 0.000000000
0.000000000 + -4.897959184t + t2 = 0 + -2.653061224
-4.897959184t + t2 = 0 + -2.653061224

Combine like terms: 0 + -2.653061224 = -2.653061224
-4.897959184t + t2 = -2.653061224

The t term is -4.897959184t.  Take half its coefficient (-2.448979592).
Square it (5.997501042) and add it to both sides.

Add '5.997501042' to each side of the equation.
-4.897959184t + 5.997501042 + t2 = -2.653061224 + 5.997501042

Reorder the terms:
5.997501042 + -4.897959184t + t2 = -2.653061224 + 5.997501042

Combine like terms: -2.653061224 + 5.997501042 = 3.344439818
5.997501042 + -4.897959184t + t2 = 3.344439818

Factor a perfect square on the left side:
(t + -2.448979592)(t + -2.448979592) = 3.344439818

Calculate the square root of the right side: 1.828780965

Break this problem into two subproblems by setting 
(t + -2.448979592) equal to 1.828780965 and -1.828780965.


Subproblem 1
t + -2.448979592 = 1.828780965

Simplifying
t + -2.448979592 = 1.828780965

Reorder the terms:
-2.448979592 + t = 1.828780965

Solving
-2.448979592 + t = 1.828780965

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '2.448979592' to each side of the equation.
-2.448979592 + 2.448979592 + t = 1.828780965 + 2.448979592

Combine like terms: -2.448979592 + 2.448979592 = 0.000000000
0.000000000 + t = 1.828780965 + 2.448979592
t = 1.828780965 + 2.448979592

Combine like terms: 1.828780965 + 2.448979592 = 4.277760557
t = 4.277760557

Simplifying
t = 4.277760557


Subproblem 2
t + -2.448979592 = -1.828780965

Simplifying
t + -2.448979592 = -1.828780965

Reorder the terms:
-2.448979592 + t = -1.828780965

Solving
-2.448979592 + t = -1.828780965

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '2.448979592' to each side of the equation.
-2.448979592 + 2.448979592 + t = -1.828780965 + 2.448979592

Combine like terms: -2.448979592 + 2.448979592 = 0.000000000
0.000000000 + t = -1.828780965 + 2.448979592
t = -1.828780965 + 2.448979592

Combine like terms: -1.828780965 + 2.448979592 = 0.620198627
t = 0.620198627

Simplifying
t = 0.620198627


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.277760557, 0.620198627}

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