2.5t^2+80t=1000

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Solution for 2.5t^2+80t=1000 equation:


Simplifying
2.5t2 + 80t = 1000

Reorder the terms:
80t + 2.5t2 = 1000

Solving
80t + 2.5t2 = 1000

Solving for variable 't'.

Reorder the terms:
-1000 + 80t + 2.5t2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 80t + 2.5t2 = 0

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

Divide each side by '2.5'.
-400 + 32t + t2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 32t + 400 + t2 = 0 + 400

Reorder the terms:
-400 + 400 + 32t + t2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 32t + t2 = 0 + 400
32t + t2 = 0 + 400

Combine like terms: 0 + 400 = 400
32t + t2 = 400

The t term is 32t.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32t + 256 + t2 = 400 + 256

Reorder the terms:
256 + 32t + t2 = 400 + 256

Combine like terms: 400 + 256 = 656
256 + 32t + t2 = 656

Factor a perfect square on the left side:
(t + 16)(t + 16) = 656

Calculate the square root of the right side: 25.61249695

Break this problem into two subproblems by setting 
(t + 16) equal to 25.61249695 and -25.61249695.

Subproblem 1

t + 16 = 25.61249695 Simplifying t + 16 = 25.61249695 Reorder the terms: 16 + t = 25.61249695 Solving 16 + t = 25.61249695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = 25.61249695 + -16 Combine like terms: 16 + -16 = 0 0 + t = 25.61249695 + -16 t = 25.61249695 + -16 Combine like terms: 25.61249695 + -16 = 9.61249695 t = 9.61249695 Simplifying t = 9.61249695

Subproblem 2

t + 16 = -25.61249695 Simplifying t + 16 = -25.61249695 Reorder the terms: 16 + t = -25.61249695 Solving 16 + t = -25.61249695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = -25.61249695 + -16 Combine like terms: 16 + -16 = 0 0 + t = -25.61249695 + -16 t = -25.61249695 + -16 Combine like terms: -25.61249695 + -16 = -41.61249695 t = -41.61249695 Simplifying t = -41.61249695

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.61249695, -41.61249695}

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