t^2+4.5t-35=0

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Solution for t^2+4.5t-35=0 equation: 


Simplifying
t2 + 4.5t + -35 = 0

Reorder the terms:
-35 + 4.5t + t2 = 0

Solving
-35 + 4.5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 4.5t + 35 + t2 = 0 + 35

Reorder the terms:
-35 + 35 + 4.5t + t2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 4.5t + t2 = 0 + 35
4.5t + t2 = 0 + 35

Combine like terms: 0 + 35 = 35
4.5t + t2 = 35

The t term is 4.5t.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5t + 5.0625 + t2 = 35 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = 35 + 5.0625

Combine like terms: 35 + 5.0625 = 40.0625
5.0625 + 4.5t + t2 = 40.0625

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 40.0625

Calculate the square root of the right side: 6.329494451

Break this problem into two subproblems by setting 
(t + 2.25) equal to 6.329494451 and -6.329494451.


Subproblem 1
t + 2.25 = 6.329494451

Simplifying
t + 2.25 = 6.329494451

Reorder the terms:
2.25 + t = 6.329494451

Solving
2.25 + t = 6.329494451

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = 6.329494451 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 6.329494451 + -2.25
t = 6.329494451 + -2.25

Combine like terms: 6.329494451 + -2.25 = 4.079494451
t = 4.079494451

Simplifying
t = 4.079494451


Subproblem 2
t + 2.25 = -6.329494451

Simplifying
t + 2.25 = -6.329494451

Reorder the terms:
2.25 + t = -6.329494451

Solving
2.25 + t = -6.329494451

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = -6.329494451 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -6.329494451 + -2.25
t = -6.329494451 + -2.25

Combine like terms: -6.329494451 + -2.25 = -8.579494451
t = -8.579494451

Simplifying
t = -8.579494451


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.079494451, -8.579494451}

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