4x^2+72x-696=0

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Solution for 4x^2+72x-696=0 equation: 


Simplifying
4x2 + 72x + -696 = 0

Reorder the terms:
-696 + 72x + 4x2 = 0

Solving
-696 + 72x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-174 + 18x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-174 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
-174 + 18x + x2 = 0

Solving
-174 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '174' to each side of the equation.
-174 + 18x + 174 + x2 = 0 + 174

Reorder the terms:
-174 + 174 + 18x + x2 = 0 + 174

Combine like terms: -174 + 174 = 0
0 + 18x + x2 = 0 + 174
18x + x2 = 0 + 174

Combine like terms: 0 + 174 = 174
18x + x2 = 174

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 174 + 81

Reorder the terms:
81 + 18x + x2 = 174 + 81

Combine like terms: 174 + 81 = 255
81 + 18x + x2 = 255

Factor a perfect square on the left side:
(x + 9)(x + 9) = 255

Calculate the square root of the right side: 15.968719423

Break this problem into two subproblems by setting 
(x + 9) equal to 15.968719423 and -15.968719423.


Subproblem 1
x + 9 = 15.968719423

Simplifying
x + 9 = 15.968719423

Reorder the terms:
9 + x = 15.968719423

Solving
9 + x = 15.968719423

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 15.968719423 + -9

Combine like terms: 9 + -9 = 0
0 + x = 15.968719423 + -9
x = 15.968719423 + -9

Combine like terms: 15.968719423 + -9 = 6.968719423
x = 6.968719423

Simplifying
x = 6.968719423


Subproblem 2
x + 9 = -15.968719423

Simplifying
x + 9 = -15.968719423

Reorder the terms:
9 + x = -15.968719423

Solving
9 + x = -15.968719423

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -15.968719423 + -9

Combine like terms: 9 + -9 = 0
0 + x = -15.968719423 + -9
x = -15.968719423 + -9

Combine like terms: -15.968719423 + -9 = -24.968719423
x = -24.968719423

Simplifying
x = -24.968719423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.968719423, -24.968719423}
Solution
x = {6.968719423, -24.968719423}

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