t^2+5t-28=0

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Solution for t^2+5t-28=0 equation: 


Simplifying
t2 + 5t + -28 = 0

Reorder the terms:
-28 + 5t + t2 = 0

Solving
-28 + 5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 5t + 28 + t2 = 0 + 28

Reorder the terms:
-28 + 28 + 5t + t2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 5t + t2 = 0 + 28
5t + t2 = 0 + 28

Combine like terms: 0 + 28 = 28
5t + t2 = 28

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = 28 + 6.25

Reorder the terms:
6.25 + 5t + t2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + 5t + t2 = 34.25

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(t + 2.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
t + 2.5 = 5.852349955

Simplifying
t + 2.5 = 5.852349955

Reorder the terms:
2.5 + t = 5.852349955

Solving
2.5 + t = 5.852349955

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 5.852349955 + -2.5
t = 5.852349955 + -2.5

Combine like terms: 5.852349955 + -2.5 = 3.352349955
t = 3.352349955

Simplifying
t = 3.352349955


Subproblem 2
t + 2.5 = -5.852349955

Simplifying
t + 2.5 = -5.852349955

Reorder the terms:
2.5 + t = -5.852349955

Solving
2.5 + t = -5.852349955

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -5.852349955 + -2.5
t = -5.852349955 + -2.5

Combine like terms: -5.852349955 + -2.5 = -8.352349955
t = -8.352349955

Simplifying
t = -8.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.352349955, -8.352349955}

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