-4.9t^2-20t+300=0

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Solution for -4.9t^2-20t+300=0 equation:


Simplifying
-4.9t2 + -20t + 300 = 0

Reorder the terms:
300 + -20t + -4.9t2 = 0

Solving
300 + -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'.
-61.2244898 + 4.081632653t + t2 = 0

Move the constant term to the right:

Add '61.2244898' to each side of the equation.
-61.2244898 + 4.081632653t + 61.2244898 + t2 = 0 + 61.2244898

Reorder the terms:
-61.2244898 + 61.2244898 + 4.081632653t + t2 = 0 + 61.2244898

Combine like terms: -61.2244898 + 61.2244898 = 0.0000000
0.0000000 + 4.081632653t + t2 = 0 + 61.2244898
4.081632653t + t2 = 0 + 61.2244898

Combine like terms: 0 + 61.2244898 = 61.2244898
4.081632653t + t2 = 61.2244898

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 = 61.2244898 + 4.164931281

Reorder the terms:
4.164931281 + 4.081632653t + t2 = 61.2244898 + 4.164931281

Combine like terms: 61.2244898 + 4.164931281 = 65.389421081
4.164931281 + 4.081632653t + t2 = 65.389421081

Factor a perfect square on the left side:
(t + 2.040816327)(t + 2.040816327) = 65.389421081

Calculate the square root of the right side: 8.086372554

Break this problem into two subproblems by setting 
(t + 2.040816327) equal to 8.086372554 and -8.086372554.

Subproblem 1

t + 2.040816327 = 8.086372554 Simplifying t + 2.040816327 = 8.086372554 Reorder the terms: 2.040816327 + t = 8.086372554 Solving 2.040816327 + t = 8.086372554 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 = 8.086372554 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 8.086372554 + -2.040816327 t = 8.086372554 + -2.040816327 Combine like terms: 8.086372554 + -2.040816327 = 6.045556227 t = 6.045556227 Simplifying t = 6.045556227

Subproblem 2

t + 2.040816327 = -8.086372554 Simplifying t + 2.040816327 = -8.086372554 Reorder the terms: 2.040816327 + t = -8.086372554 Solving 2.040816327 + t = -8.086372554 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 = -8.086372554 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -8.086372554 + -2.040816327 t = -8.086372554 + -2.040816327 Combine like terms: -8.086372554 + -2.040816327 = -10.127188881 t = -10.127188881 Simplifying t = -10.127188881

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.045556227, -10.127188881}

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