-50=20t-4.9t^2

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Solution for -50=20t-4.9t^2 equation:


Simplifying
-50 = 20t + -4.9t2

Solving
-50 = 20t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-50 + -20t + 4.9t2 = 20t + -20t + -4.9t2 + 4.9t2

Combine like terms: 20t + -20t = 0
-50 + -20t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-50 + -20t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-50 + -20t + 4.9t2 = 0.0

Begin completing the square.  Divide all terms by
4.9 the coefficient of the squared term: 

Divide each side by '4.9'.
-10.20408163 + -4.081632653t + t2 = 0

Move the constant term to the right:

Add '10.20408163' to each side of the equation.
-10.20408163 + -4.081632653t + 10.20408163 + t2 = 0 + 10.20408163

Reorder the terms:
-10.20408163 + 10.20408163 + -4.081632653t + t2 = 0 + 10.20408163

Combine like terms: -10.20408163 + 10.20408163 = 0.00000000
0.00000000 + -4.081632653t + t2 = 0 + 10.20408163
-4.081632653t + t2 = 0 + 10.20408163

Combine like terms: 0 + 10.20408163 = 10.20408163
-4.081632653t + t2 = 10.20408163

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 = 10.20408163 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653t + t2 = 10.20408163 + 4.164931281

Combine like terms: 10.20408163 + 4.164931281 = 14.369012911
4.164931281 + -4.081632653t + t2 = 14.369012911

Factor a perfect square on the left side:
(t + -2.040816327)(t + -2.040816327) = 14.369012911

Calculate the square root of the right side: 3.790648086

Break this problem into two subproblems by setting 
(t + -2.040816327) equal to 3.790648086 and -3.790648086.

Subproblem 1

t + -2.040816327 = 3.790648086 Simplifying t + -2.040816327 = 3.790648086 Reorder the terms: -2.040816327 + t = 3.790648086 Solving -2.040816327 + t = 3.790648086 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 = 3.790648086 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 3.790648086 + 2.040816327 t = 3.790648086 + 2.040816327 Combine like terms: 3.790648086 + 2.040816327 = 5.831464413 t = 5.831464413 Simplifying t = 5.831464413

Subproblem 2

t + -2.040816327 = -3.790648086 Simplifying t + -2.040816327 = -3.790648086 Reorder the terms: -2.040816327 + t = -3.790648086 Solving -2.040816327 + t = -3.790648086 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 = -3.790648086 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -3.790648086 + 2.040816327 t = -3.790648086 + 2.040816327 Combine like terms: -3.790648086 + 2.040816327 = -1.749831759 t = -1.749831759 Simplifying t = -1.749831759

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.831464413, -1.749831759}

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