427.5=t^2+55t

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Solution for 427.5=t^2+55t equation:


Simplifying
427.5 = t2 + 55t

Reorder the terms:
427.5 = 55t + t2

Solving
427.5 = 55t + t2

Solving for variable 't'.

Reorder the terms:
427.5 + -55t + -1t2 = 55t + -55t + t2 + -1t2

Combine like terms: 55t + -55t = 0
427.5 + -55t + -1t2 = 0 + t2 + -1t2
427.5 + -55t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
427.5 + -55t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-427.5 + 55t + t2 = 0

Move the constant term to the right:

Add '427.5' to each side of the equation.
-427.5 + 55t + 427.5 + t2 = 0 + 427.5

Reorder the terms:
-427.5 + 427.5 + 55t + t2 = 0 + 427.5

Combine like terms: -427.5 + 427.5 = 0.0
0.0 + 55t + t2 = 0 + 427.5
55t + t2 = 0 + 427.5

Combine like terms: 0 + 427.5 = 427.5
55t + t2 = 427.5

The t term is 55t.  Take half its coefficient (27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
55t + 756.25 + t2 = 427.5 + 756.25

Reorder the terms:
756.25 + 55t + t2 = 427.5 + 756.25

Combine like terms: 427.5 + 756.25 = 1183.75
756.25 + 55t + t2 = 1183.75

Factor a perfect square on the left side:
(t + 27.5)(t + 27.5) = 1183.75

Calculate the square root of the right side: 34.405668138

Break this problem into two subproblems by setting 
(t + 27.5) equal to 34.405668138 and -34.405668138.

Subproblem 1

t + 27.5 = 34.405668138 Simplifying t + 27.5 = 34.405668138 Reorder the terms: 27.5 + t = 34.405668138 Solving 27.5 + t = 34.405668138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + t = 34.405668138 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + t = 34.405668138 + -27.5 t = 34.405668138 + -27.5 Combine like terms: 34.405668138 + -27.5 = 6.905668138 t = 6.905668138 Simplifying t = 6.905668138

Subproblem 2

t + 27.5 = -34.405668138 Simplifying t + 27.5 = -34.405668138 Reorder the terms: 27.5 + t = -34.405668138 Solving 27.5 + t = -34.405668138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + t = -34.405668138 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + t = -34.405668138 + -27.5 t = -34.405668138 + -27.5 Combine like terms: -34.405668138 + -27.5 = -61.905668138 t = -61.905668138 Simplifying t = -61.905668138

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.905668138, -61.905668138}

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