4.9t^2+2t=800

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Solution for 4.9t^2+2t=800 equation:


Simplifying
4.9t2 + 2t = 800

Reorder the terms:
2t + 4.9t2 = 800

Solving
2t + 4.9t2 = 800

Solving for variable 't'.

Reorder the terms:
-800 + 2t + 4.9t2 = 800 + -800

Combine like terms: 800 + -800 = 0
-800 + 2t + 4.9t2 = 0

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

Divide each side by '4.9'.
-163.2653061 + 0.4081632653t + t2 = 0

Move the constant term to the right:

Add '163.2653061' to each side of the equation.
-163.2653061 + 0.4081632653t + 163.2653061 + t2 = 0 + 163.2653061

Reorder the terms:
-163.2653061 + 163.2653061 + 0.4081632653t + t2 = 0 + 163.2653061

Combine like terms: -163.2653061 + 163.2653061 = 0.0000000
0.0000000 + 0.4081632653t + t2 = 0 + 163.2653061
0.4081632653t + t2 = 0 + 163.2653061

Combine like terms: 0 + 163.2653061 = 163.2653061
0.4081632653t + t2 = 163.2653061

The t term is 0.4081632653t.  Take half its coefficient (0.2040816327).
Square it (0.04164931281) and add it to both sides.

Add '0.04164931281' to each side of the equation.
0.4081632653t + 0.04164931281 + t2 = 163.2653061 + 0.04164931281

Reorder the terms:
0.04164931281 + 0.4081632653t + t2 = 163.2653061 + 0.04164931281

Combine like terms: 163.2653061 + 0.04164931281 = 163.30695541281
0.04164931281 + 0.4081632653t + t2 = 163.30695541281

Factor a perfect square on the left side:
(t + 0.2040816327)(t + 0.2040816327) = 163.30695541281

Calculate the square root of the right side: 12.779160982

Break this problem into two subproblems by setting 
(t + 0.2040816327) equal to 12.779160982 and -12.779160982.

Subproblem 1

t + 0.2040816327 = 12.779160982 Simplifying t + 0.2040816327 = 12.779160982 Reorder the terms: 0.2040816327 + t = 12.779160982 Solving 0.2040816327 + t = 12.779160982 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + t = 12.779160982 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 12.779160982 + -0.2040816327 t = 12.779160982 + -0.2040816327 Combine like terms: 12.779160982 + -0.2040816327 = 12.5750793493 t = 12.5750793493 Simplifying t = 12.5750793493

Subproblem 2

t + 0.2040816327 = -12.779160982 Simplifying t + 0.2040816327 = -12.779160982 Reorder the terms: 0.2040816327 + t = -12.779160982 Solving 0.2040816327 + t = -12.779160982 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + t = -12.779160982 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -12.779160982 + -0.2040816327 t = -12.779160982 + -0.2040816327 Combine like terms: -12.779160982 + -0.2040816327 = -12.9832426147 t = -12.9832426147 Simplifying t = -12.9832426147

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.5750793493, -12.9832426147}

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