4x^2+16x-148=0

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Solution for 4x^2+16x-148=0 equation: 


Simplifying
4x2 + 16x + -148 = 0

Reorder the terms:
-148 + 16x + 4x2 = 0

Solving
-148 + 16x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-37 + 4x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-37 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-37 + 4x + x2 = 0

Solving
-37 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 4x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 4x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 4x + x2 = 0 + 37
4x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
4x + x2 = 37

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 37 + 4

Reorder the terms:
4 + 4x + x2 = 37 + 4

Combine like terms: 37 + 4 = 41
4 + 4x + x2 = 41

Factor a perfect square on the left side:
(x + 2)(x + 2) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 2) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 2 = 6.403124237

Simplifying
x + 2 = 6.403124237

Reorder the terms:
2 + x = 6.403124237

Solving
2 + x = 6.403124237

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.403124237 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.403124237 + -2
x = 6.403124237 + -2

Combine like terms: 6.403124237 + -2 = 4.403124237
x = 4.403124237

Simplifying
x = 4.403124237


Subproblem 2
x + 2 = -6.403124237

Simplifying
x + 2 = -6.403124237

Reorder the terms:
2 + x = -6.403124237

Solving
2 + x = -6.403124237

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.403124237 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.403124237 + -2
x = -6.403124237 + -2

Combine like terms: -6.403124237 + -2 = -8.403124237
x = -8.403124237

Simplifying
x = -8.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.403124237, -8.403124237}
Solution
x = {4.403124237, -8.403124237}

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