4x^2-58x-54=0

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Solution for 4x^2-58x-54=0 equation: 


Simplifying
4x2 + -58x + -54 = 0

Reorder the terms:
-54 + -58x + 4x2 = 0

Solving
-54 + -58x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -29x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-27 + -29x + 2x2)' equal to zero and attempt to solve:

Simplifying
-27 + -29x + 2x2 = 0

Solving
-27 + -29x + 2x2 = 0

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

Divide each side by '2'.
-13.5 + -14.5x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -14.5x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -14.5x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -14.5x + x2 = 0 + 13.5
-14.5x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-14.5x + x2 = 13.5

The x term is -14.5x.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5x + 52.5625 + x2 = 13.5 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = 13.5 + 52.5625

Combine like terms: 13.5 + 52.5625 = 66.0625
52.5625 + -14.5x + x2 = 66.0625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 66.0625

Calculate the square root of the right side: 8.127884104

Break this problem into two subproblems by setting 
(x + -7.25) equal to 8.127884104 and -8.127884104.


Subproblem 1
x + -7.25 = 8.127884104

Simplifying
x + -7.25 = 8.127884104

Reorder the terms:
-7.25 + x = 8.127884104

Solving
-7.25 + x = 8.127884104

Solving for variable 'x'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + x = 8.127884104 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + x = 8.127884104 + 7.25
x = 8.127884104 + 7.25

Combine like terms: 8.127884104 + 7.25 = 15.377884104
x = 15.377884104

Simplifying
x = 15.377884104


Subproblem 2
x + -7.25 = -8.127884104

Simplifying
x + -7.25 = -8.127884104

Reorder the terms:
-7.25 + x = -8.127884104

Solving
-7.25 + x = -8.127884104

Solving for variable 'x'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + x = -8.127884104 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + x = -8.127884104 + 7.25
x = -8.127884104 + 7.25

Combine like terms: -8.127884104 + 7.25 = -0.877884104
x = -0.877884104

Simplifying
x = -0.877884104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.377884104, -0.877884104}
Solution
x = {15.377884104, -0.877884104}

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