8=15t+5t^2

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Solution for 8=15t+5t^2 equation:


Simplifying
8 = 15t + 5t2

Solving
8 = 15t + 5t2

Solving for variable 't'.

Reorder the terms:
8 + -15t + -5t2 = 15t + -15t + 5t2 + -5t2

Combine like terms: 15t + -15t = 0
8 + -15t + -5t2 = 0 + 5t2 + -5t2
8 + -15t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
8 + -15t + -5t2 = 0

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

Divide each side by '-5'.
-1.6 + 3t + t2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 3t + 1.6 + t2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 3t + t2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 3t + t2 = 0 + 1.6
3t + t2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
3t + t2 = 1.6

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 = 1.6 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 1.6 + 2.25

Combine like terms: 1.6 + 2.25 = 3.85
2.25 + 3t + t2 = 3.85

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(t + 1.5) equal to 1.962141687 and -1.962141687.

Subproblem 1

t + 1.5 = 1.962141687 Simplifying t + 1.5 = 1.962141687 Reorder the terms: 1.5 + t = 1.962141687 Solving 1.5 + t = 1.962141687 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 = 1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 1.962141687 + -1.5 t = 1.962141687 + -1.5 Combine like terms: 1.962141687 + -1.5 = 0.462141687 t = 0.462141687 Simplifying t = 0.462141687

Subproblem 2

t + 1.5 = -1.962141687 Simplifying t + 1.5 = -1.962141687 Reorder the terms: 1.5 + t = -1.962141687 Solving 1.5 + t = -1.962141687 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 = -1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -1.962141687 + -1.5 t = -1.962141687 + -1.5 Combine like terms: -1.962141687 + -1.5 = -3.462141687 t = -3.462141687 Simplifying t = -3.462141687

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.462141687, -3.462141687}

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