4.9t^2-12t+5=0

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Solution for 4.9t^2-12t+5=0 equation:


Simplifying
4.9t2 + -12t + 5 = 0

Reorder the terms:
5 + -12t + 4.9t2 = 0

Solving
5 + -12t + 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'.
1.020408163 + -2.448979592t + t2 = 0

Move the constant term to the right:

Add '-1.020408163' to each side of the equation.
1.020408163 + -2.448979592t + -1.020408163 + t2 = 0 + -1.020408163

Reorder the terms:
1.020408163 + -1.020408163 + -2.448979592t + t2 = 0 + -1.020408163

Combine like terms: 1.020408163 + -1.020408163 = 0.000000000
0.000000000 + -2.448979592t + t2 = 0 + -1.020408163
-2.448979592t + t2 = 0 + -1.020408163

Combine like terms: 0 + -1.020408163 = -1.020408163
-2.448979592t + t2 = -1.020408163

The t term is -2.448979592t.  Take half its coefficient (-1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
-2.448979592t + 1.499375261 + t2 = -1.020408163 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592t + t2 = -1.020408163 + 1.499375261

Combine like terms: -1.020408163 + 1.499375261 = 0.478967098
1.499375261 + -2.448979592t + t2 = 0.478967098

Factor a perfect square on the left side:
(t + -1.224489796)(t + -1.224489796) = 0.478967098

Calculate the square root of the right side: 0.692074489

Break this problem into two subproblems by setting 
(t + -1.224489796) equal to 0.692074489 and -0.692074489.

Subproblem 1

t + -1.224489796 = 0.692074489 Simplifying t + -1.224489796 = 0.692074489 Reorder the terms: -1.224489796 + t = 0.692074489 Solving -1.224489796 + t = 0.692074489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 0.692074489 + 1.224489796 t = 0.692074489 + 1.224489796 Combine like terms: 0.692074489 + 1.224489796 = 1.916564285 t = 1.916564285 Simplifying t = 1.916564285

Subproblem 2

t + -1.224489796 = -0.692074489 Simplifying t + -1.224489796 = -0.692074489 Reorder the terms: -1.224489796 + t = -0.692074489 Solving -1.224489796 + t = -0.692074489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -0.692074489 + 1.224489796 t = -0.692074489 + 1.224489796 Combine like terms: -0.692074489 + 1.224489796 = 0.532415307 t = 0.532415307 Simplifying t = 0.532415307

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.916564285, 0.532415307}

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