4.9t^2-20t+8=0

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Solution for 4.9t^2-20t+8=0 equation:


Simplifying
4.9t2 + -20t + 8 = 0

Reorder the terms:
8 + -20t + 4.9t2 = 0

Solving
8 + -20t + 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'.
1.632653061 + -4.081632653t + t2 = 0

Move the constant term to the right:

Add '-1.632653061' to each side of the equation.
1.632653061 + -4.081632653t + -1.632653061 + t2 = 0 + -1.632653061

Reorder the terms:
1.632653061 + -1.632653061 + -4.081632653t + t2 = 0 + -1.632653061

Combine like terms: 1.632653061 + -1.632653061 = 0.000000000
0.000000000 + -4.081632653t + t2 = 0 + -1.632653061
-4.081632653t + t2 = 0 + -1.632653061

Combine like terms: 0 + -1.632653061 = -1.632653061
-4.081632653t + t2 = -1.632653061

The t term is -4.081632653t.  Take half its coefficient (-2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
-4.081632653t + 4.164931281 + t2 = -1.632653061 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653t + t2 = -1.632653061 + 4.164931281

Combine like terms: -1.632653061 + 4.164931281 = 2.53227822
4.164931281 + -4.081632653t + t2 = 2.53227822

Factor a perfect square on the left side:
(t + -2.040816327)(t + -2.040816327) = 2.53227822

Calculate the square root of the right side: 1.591313363

Break this problem into two subproblems by setting 
(t + -2.040816327) equal to 1.591313363 and -1.591313363.

Subproblem 1

t + -2.040816327 = 1.591313363 Simplifying t + -2.040816327 = 1.591313363 Reorder the terms: -2.040816327 + t = 1.591313363 Solving -2.040816327 + t = 1.591313363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = 1.591313363 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 1.591313363 + 2.040816327 t = 1.591313363 + 2.040816327 Combine like terms: 1.591313363 + 2.040816327 = 3.63212969 t = 3.63212969 Simplifying t = 3.63212969

Subproblem 2

t + -2.040816327 = -1.591313363 Simplifying t + -2.040816327 = -1.591313363 Reorder the terms: -2.040816327 + t = -1.591313363 Solving -2.040816327 + t = -1.591313363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = -1.591313363 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -1.591313363 + 2.040816327 t = -1.591313363 + 2.040816327 Combine like terms: -1.591313363 + 2.040816327 = 0.449502964 t = 0.449502964 Simplifying t = 0.449502964

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.63212969, 0.449502964}

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