-4.9t^2+20t+40=0

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Solution for -4.9t^2+20t+40=0 equation:


Simplifying
-4.9t2 + 20t + 40 = 0

Reorder the terms:
40 + 20t + -4.9t2 = 0

Solving
40 + 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'.
-8.163265306 + -4.081632653t + t2 = 0

Move the constant term to the right:

Add '8.163265306' to each side of the equation.
-8.163265306 + -4.081632653t + 8.163265306 + t2 = 0 + 8.163265306

Reorder the terms:
-8.163265306 + 8.163265306 + -4.081632653t + t2 = 0 + 8.163265306

Combine like terms: -8.163265306 + 8.163265306 = 0.000000000
0.000000000 + -4.081632653t + t2 = 0 + 8.163265306
-4.081632653t + t2 = 0 + 8.163265306

Combine like terms: 0 + 8.163265306 = 8.163265306
-4.081632653t + t2 = 8.163265306

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 = 8.163265306 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653t + t2 = 8.163265306 + 4.164931281

Combine like terms: 8.163265306 + 4.164931281 = 12.328196587
4.164931281 + -4.081632653t + t2 = 12.328196587

Factor a perfect square on the left side:
(t + -2.040816327)(t + -2.040816327) = 12.328196587

Calculate the square root of the right side: 3.511153171

Break this problem into two subproblems by setting 
(t + -2.040816327) equal to 3.511153171 and -3.511153171.

Subproblem 1

t + -2.040816327 = 3.511153171 Simplifying t + -2.040816327 = 3.511153171 Reorder the terms: -2.040816327 + t = 3.511153171 Solving -2.040816327 + t = 3.511153171 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 = 3.511153171 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 3.511153171 + 2.040816327 t = 3.511153171 + 2.040816327 Combine like terms: 3.511153171 + 2.040816327 = 5.551969498 t = 5.551969498 Simplifying t = 5.551969498

Subproblem 2

t + -2.040816327 = -3.511153171 Simplifying t + -2.040816327 = -3.511153171 Reorder the terms: -2.040816327 + t = -3.511153171 Solving -2.040816327 + t = -3.511153171 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 = -3.511153171 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -3.511153171 + 2.040816327 t = -3.511153171 + 2.040816327 Combine like terms: -3.511153171 + 2.040816327 = -1.470336844 t = -1.470336844 Simplifying t = -1.470336844

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.551969498, -1.470336844}

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