t^2+40t=80000

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Solution for t^2+40t=80000 equation:


Simplifying
t2 + 40t = 80000

Reorder the terms:
40t + t2 = 80000

Solving
40t + t2 = 80000

Solving for variable 't'.

Reorder the terms:
-80000 + 40t + t2 = 80000 + -80000

Combine like terms: 80000 + -80000 = 0
-80000 + 40t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80000' to each side of the equation.
-80000 + 40t + 80000 + t2 = 0 + 80000

Reorder the terms:
-80000 + 80000 + 40t + t2 = 0 + 80000

Combine like terms: -80000 + 80000 = 0
0 + 40t + t2 = 0 + 80000
40t + t2 = 0 + 80000

Combine like terms: 0 + 80000 = 80000
40t + t2 = 80000

The t term is 40t.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40t + 400 + t2 = 80000 + 400

Reorder the terms:
400 + 40t + t2 = 80000 + 400

Combine like terms: 80000 + 400 = 80400
400 + 40t + t2 = 80400

Factor a perfect square on the left side:
(t + 20)(t + 20) = 80400

Calculate the square root of the right side: 283.548937575

Break this problem into two subproblems by setting 
(t + 20) equal to 283.548937575 and -283.548937575.

Subproblem 1

t + 20 = 283.548937575 Simplifying t + 20 = 283.548937575 Reorder the terms: 20 + t = 283.548937575 Solving 20 + t = 283.548937575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = 283.548937575 + -20 Combine like terms: 20 + -20 = 0 0 + t = 283.548937575 + -20 t = 283.548937575 + -20 Combine like terms: 283.548937575 + -20 = 263.548937575 t = 263.548937575 Simplifying t = 263.548937575

Subproblem 2

t + 20 = -283.548937575 Simplifying t + 20 = -283.548937575 Reorder the terms: 20 + t = -283.548937575 Solving 20 + t = -283.548937575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = -283.548937575 + -20 Combine like terms: 20 + -20 = 0 0 + t = -283.548937575 + -20 t = -283.548937575 + -20 Combine like terms: -283.548937575 + -20 = -303.548937575 t = -303.548937575 Simplifying t = -303.548937575

Solution

The solution to the problem is based on the solutions from the subproblems. t = {263.548937575, -303.548937575}

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