15000=2.6t+4.9(t*t)

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Solution for 15000=2.6t+4.9(t*t) equation:


Simplifying
15000 = 2.6t + 4.9(t * t)

Multiply t * t
15000 = 2.6t + 4.9(t2)

Solving
15000 = 2.6t + 4.9t2

Solving for variable 't'.

Reorder the terms:
15000 + -2.6t + -4.9t2 = 2.6t + -2.6t + 4.9t2 + -4.9t2

Combine like terms: 2.6t + -2.6t = 0.0
15000 + -2.6t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2
15000 + -2.6t + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
15000 + -2.6t + -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'.
-3061.22449 + 0.5306122449t + t2 = 0

Move the constant term to the right:

Add '3061.22449' to each side of the equation.
-3061.22449 + 0.5306122449t + 3061.22449 + t2 = 0 + 3061.22449

Reorder the terms:
-3061.22449 + 3061.22449 + 0.5306122449t + t2 = 0 + 3061.22449

Combine like terms: -3061.22449 + 3061.22449 = 0.00000
0.00000 + 0.5306122449t + t2 = 0 + 3061.22449
0.5306122449t + t2 = 0 + 3061.22449

Combine like terms: 0 + 3061.22449 = 3061.22449
0.5306122449t + t2 = 3061.22449

The t term is 0.5306122449t.  Take half its coefficient (0.2653061225).
Square it (0.07038733864) and add it to both sides.

Add '0.07038733864' to each side of the equation.
0.5306122449t + 0.07038733864 + t2 = 3061.22449 + 0.07038733864

Reorder the terms:
0.07038733864 + 0.5306122449t + t2 = 3061.22449 + 0.07038733864

Combine like terms: 3061.22449 + 0.07038733864 = 3061.29487733864
0.07038733864 + 0.5306122449t + t2 = 3061.29487733864

Factor a perfect square on the left side:
(t + 0.2653061225)(t + 0.2653061225) = 3061.29487733864

Calculate the square root of the right side: 55.328969603

Break this problem into two subproblems by setting 
(t + 0.2653061225) equal to 55.328969603 and -55.328969603.

Subproblem 1

t + 0.2653061225 = 55.328969603 Simplifying t + 0.2653061225 = 55.328969603 Reorder the terms: 0.2653061225 + t = 55.328969603 Solving 0.2653061225 + t = 55.328969603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2653061225' to each side of the equation. 0.2653061225 + -0.2653061225 + t = 55.328969603 + -0.2653061225 Combine like terms: 0.2653061225 + -0.2653061225 = 0.0000000000 0.0000000000 + t = 55.328969603 + -0.2653061225 t = 55.328969603 + -0.2653061225 Combine like terms: 55.328969603 + -0.2653061225 = 55.0636634805 t = 55.0636634805 Simplifying t = 55.0636634805

Subproblem 2

t + 0.2653061225 = -55.328969603 Simplifying t + 0.2653061225 = -55.328969603 Reorder the terms: 0.2653061225 + t = -55.328969603 Solving 0.2653061225 + t = -55.328969603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2653061225' to each side of the equation. 0.2653061225 + -0.2653061225 + t = -55.328969603 + -0.2653061225 Combine like terms: 0.2653061225 + -0.2653061225 = 0.0000000000 0.0000000000 + t = -55.328969603 + -0.2653061225 t = -55.328969603 + -0.2653061225 Combine like terms: -55.328969603 + -0.2653061225 = -55.5942757255 t = -55.5942757255 Simplifying t = -55.5942757255

Solution

The solution to the problem is based on the solutions from the subproblems. t = {55.0636634805, -55.5942757255}

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