4t+t^2=30

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Solution for 4t+t^2=30 equation: 


Simplifying
4t + t2 = 30

Solving
4t + t2 = 30

Solving for variable 't'.

Reorder the terms:
-30 + 4t + t2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4t + 30 + t2 = 0 + 30

Reorder the terms:
-30 + 30 + 4t + t2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4t + t2 = 0 + 30
4t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
4t + t2 = 30

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 30 + 4

Reorder the terms:
4 + 4t + t2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + 4t + t2 = 34

Factor a perfect square on the left side:
(t + 2)(t + 2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(t + 2) equal to 5.830951895 and -5.830951895.


Subproblem 1
t + 2 = 5.830951895

Simplifying
t + 2 = 5.830951895

Reorder the terms:
2 + t = 5.830951895

Solving
2 + t = 5.830951895

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + t = 5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + t = 5.830951895 + -2
t = 5.830951895 + -2

Combine like terms: 5.830951895 + -2 = 3.830951895
t = 3.830951895

Simplifying
t = 3.830951895


Subproblem 2
t + 2 = -5.830951895

Simplifying
t + 2 = -5.830951895

Reorder the terms:
2 + t = -5.830951895

Solving
2 + t = -5.830951895

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + t = -5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + t = -5.830951895 + -2
t = -5.830951895 + -2

Combine like terms: -5.830951895 + -2 = -7.830951895
t = -7.830951895

Simplifying
t = -7.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.830951895, -7.830951895}

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