4x^2-152x+704=0

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Solution for 4x^2-152x+704=0 equation: 


Simplifying
4x2 + -152x + 704 = 0

Reorder the terms:
704 + -152x + 4x2 = 0

Solving
704 + -152x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(176 + -38x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(176 + -38x + x2)' equal to zero and attempt to solve:

Simplifying
176 + -38x + x2 = 0

Solving
176 + -38x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-176' to each side of the equation.
176 + -38x + -176 + x2 = 0 + -176

Reorder the terms:
176 + -176 + -38x + x2 = 0 + -176

Combine like terms: 176 + -176 = 0
0 + -38x + x2 = 0 + -176
-38x + x2 = 0 + -176

Combine like terms: 0 + -176 = -176
-38x + x2 = -176

The x term is -38x.  Take half its coefficient (-19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
-38x + 361 + x2 = -176 + 361

Reorder the terms:
361 + -38x + x2 = -176 + 361

Combine like terms: -176 + 361 = 185
361 + -38x + x2 = 185

Factor a perfect square on the left side:
(x + -19)(x + -19) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(x + -19) equal to 13.601470509 and -13.601470509.


Subproblem 1
x + -19 = 13.601470509

Simplifying
x + -19 = 13.601470509

Reorder the terms:
-19 + x = 13.601470509

Solving
-19 + x = 13.601470509

Solving for variable 'x'.

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

Add '19' to each side of the equation.
-19 + 19 + x = 13.601470509 + 19

Combine like terms: -19 + 19 = 0
0 + x = 13.601470509 + 19
x = 13.601470509 + 19

Combine like terms: 13.601470509 + 19 = 32.601470509
x = 32.601470509

Simplifying
x = 32.601470509


Subproblem 2
x + -19 = -13.601470509

Simplifying
x + -19 = -13.601470509

Reorder the terms:
-19 + x = -13.601470509

Solving
-19 + x = -13.601470509

Solving for variable 'x'.

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

Add '19' to each side of the equation.
-19 + 19 + x = -13.601470509 + 19

Combine like terms: -19 + 19 = 0
0 + x = -13.601470509 + 19
x = -13.601470509 + 19

Combine like terms: -13.601470509 + 19 = 5.398529491
x = 5.398529491

Simplifying
x = 5.398529491


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.601470509, 5.398529491}
Solution
x = {32.601470509, 5.398529491}

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