11=15t+5t^2

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Solution for 11=15t+5t^2 equation:


Simplifying
11 = 15t + 5t2

Solving
11 = 15t + 5t2

Solving for variable 't'.

Reorder the terms:
11 + -15t + -5t2 = 15t + -15t + 5t2 + -5t2

Combine like terms: 15t + -15t = 0
11 + -15t + -5t2 = 0 + 5t2 + -5t2
11 + -15t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
11 + -15t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.2 + 3t + t2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 3t + 2.2 + t2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 3t + t2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 3t + t2 = 0 + 2.2
3t + t2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
3t + t2 = 2.2

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = 2.2 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 2.2 + 2.25

Combine like terms: 2.2 + 2.25 = 4.45
2.25 + 3t + t2 = 4.45

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 4.45

Calculate the square root of the right side: 2.109502311

Break this problem into two subproblems by setting 
(t + 1.5) equal to 2.109502311 and -2.109502311.

Subproblem 1

t + 1.5 = 2.109502311 Simplifying t + 1.5 = 2.109502311 Reorder the terms: 1.5 + t = 2.109502311 Solving 1.5 + t = 2.109502311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 2.109502311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 2.109502311 + -1.5 t = 2.109502311 + -1.5 Combine like terms: 2.109502311 + -1.5 = 0.609502311 t = 0.609502311 Simplifying t = 0.609502311

Subproblem 2

t + 1.5 = -2.109502311 Simplifying t + 1.5 = -2.109502311 Reorder the terms: 1.5 + t = -2.109502311 Solving 1.5 + t = -2.109502311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -2.109502311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -2.109502311 + -1.5 t = -2.109502311 + -1.5 Combine like terms: -2.109502311 + -1.5 = -3.609502311 t = -3.609502311 Simplifying t = -3.609502311

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.609502311, -3.609502311}

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