x^2+5x-54=0

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Solution for x^2+5x-54=0 equation: 


Simplifying
x2 + 5x + -54 = 0

Reorder the terms:
-54 + 5x + x2 = 0

Solving
-54 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 5x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 5x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 5x + x2 = 0 + 54
5x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
5x + x2 = 54

The x term is 5x.  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.
5x + 6.25 + x2 = 54 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 54 + 6.25

Combine like terms: 54 + 6.25 = 60.25
6.25 + 5x + x2 = 60.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
x + 2.5 = 7.762087348

Simplifying
x + 2.5 = 7.762087348

Reorder the terms:
2.5 + x = 7.762087348

Solving
2.5 + x = 7.762087348

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 7.762087348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.762087348 + -2.5
x = 7.762087348 + -2.5

Combine like terms: 7.762087348 + -2.5 = 5.262087348
x = 5.262087348

Simplifying
x = 5.262087348


Subproblem 2
x + 2.5 = -7.762087348

Simplifying
x + 2.5 = -7.762087348

Reorder the terms:
2.5 + x = -7.762087348

Solving
2.5 + x = -7.762087348

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -7.762087348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.762087348 + -2.5
x = -7.762087348 + -2.5

Combine like terms: -7.762087348 + -2.5 = -10.262087348
x = -10.262087348

Simplifying
x = -10.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.262087348, -10.262087348}

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