-4.9t^2+250t+150=0

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Solution for -4.9t^2+250t+150=0 equation:


Simplifying
-4.9t2 + 250t + 150 = 0

Reorder the terms:
150 + 250t + -4.9t2 = 0

Solving
150 + 250t + -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'.
-30.6122449 + -51.02040816t + t2 = 0

Move the constant term to the right:

Add '30.6122449' to each side of the equation.
-30.6122449 + -51.02040816t + 30.6122449 + t2 = 0 + 30.6122449

Reorder the terms:
-30.6122449 + 30.6122449 + -51.02040816t + t2 = 0 + 30.6122449

Combine like terms: -30.6122449 + 30.6122449 = 0.0000000
0.0000000 + -51.02040816t + t2 = 0 + 30.6122449
-51.02040816t + t2 = 0 + 30.6122449

Combine like terms: 0 + 30.6122449 = 30.6122449
-51.02040816t + t2 = 30.6122449

The t term is -51.02040816t.  Take half its coefficient (-25.51020408).
Square it (650.7705122) and add it to both sides.

Add '650.7705122' to each side of the equation.
-51.02040816t + 650.7705122 + t2 = 30.6122449 + 650.7705122

Reorder the terms:
650.7705122 + -51.02040816t + t2 = 30.6122449 + 650.7705122

Combine like terms: 30.6122449 + 650.7705122 = 681.3827571
650.7705122 + -51.02040816t + t2 = 681.3827571

Factor a perfect square on the left side:
(t + -25.51020408)(t + -25.51020408) = 681.3827571

Calculate the square root of the right side: 26.103309313

Break this problem into two subproblems by setting 
(t + -25.51020408) equal to 26.103309313 and -26.103309313.

Subproblem 1

t + -25.51020408 = 26.103309313 Simplifying t + -25.51020408 = 26.103309313 Reorder the terms: -25.51020408 + t = 26.103309313 Solving -25.51020408 + t = 26.103309313 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.51020408' to each side of the equation. -25.51020408 + 25.51020408 + t = 26.103309313 + 25.51020408 Combine like terms: -25.51020408 + 25.51020408 = 0.00000000 0.00000000 + t = 26.103309313 + 25.51020408 t = 26.103309313 + 25.51020408 Combine like terms: 26.103309313 + 25.51020408 = 51.613513393 t = 51.613513393 Simplifying t = 51.613513393

Subproblem 2

t + -25.51020408 = -26.103309313 Simplifying t + -25.51020408 = -26.103309313 Reorder the terms: -25.51020408 + t = -26.103309313 Solving -25.51020408 + t = -26.103309313 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.51020408' to each side of the equation. -25.51020408 + 25.51020408 + t = -26.103309313 + 25.51020408 Combine like terms: -25.51020408 + 25.51020408 = 0.00000000 0.00000000 + t = -26.103309313 + 25.51020408 t = -26.103309313 + 25.51020408 Combine like terms: -26.103309313 + 25.51020408 = -0.593105233 t = -0.593105233 Simplifying t = -0.593105233

Solution

The solution to the problem is based on the solutions from the subproblems. t = {51.613513393, -0.593105233}

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