x^2+35x-54=0

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Solution for x^2+35x-54=0 equation: 


Simplifying
x2 + 35x + -54 = 0

Reorder the terms:
-54 + 35x + x2 = 0

Solving
-54 + 35x + 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 + 35x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 35x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 35x + x2 = 0 + 54
35x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
35x + x2 = 54

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 54 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 54 + 306.25

Combine like terms: 54 + 306.25 = 360.25
306.25 + 35x + x2 = 360.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 360.25

Calculate the square root of the right side: 18.980252896

Break this problem into two subproblems by setting 
(x + 17.5) equal to 18.980252896 and -18.980252896.


Subproblem 1
x + 17.5 = 18.980252896

Simplifying
x + 17.5 = 18.980252896

Reorder the terms:
17.5 + x = 18.980252896

Solving
17.5 + x = 18.980252896

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 18.980252896 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 18.980252896 + -17.5
x = 18.980252896 + -17.5

Combine like terms: 18.980252896 + -17.5 = 1.480252896
x = 1.480252896

Simplifying
x = 1.480252896


Subproblem 2
x + 17.5 = -18.980252896

Simplifying
x + 17.5 = -18.980252896

Reorder the terms:
17.5 + x = -18.980252896

Solving
17.5 + x = -18.980252896

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -18.980252896 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -18.980252896 + -17.5
x = -18.980252896 + -17.5

Combine like terms: -18.980252896 + -17.5 = -36.480252896
x = -36.480252896

Simplifying
x = -36.480252896


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.480252896, -36.480252896}

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