16x^2+144x-224=0

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Solution for 16x^2+144x-224=0 equation: 


Simplifying
16x2 + 144x + -224 = 0

Reorder the terms:
-224 + 144x + 16x2 = 0

Solving
-224 + 144x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-14 + 9x + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-14 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + 9x + x2 = 0

Solving
-14 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 9x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 9x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 9x + x2 = 0 + 14
9x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
9x + x2 = 14

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 14 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 14 + 20.25

Combine like terms: 14 + 20.25 = 34.25
20.25 + 9x + x2 = 34.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
x + 4.5 = 5.852349955

Simplifying
x + 4.5 = 5.852349955

Reorder the terms:
4.5 + x = 5.852349955

Solving
4.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.852349955 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.852349955 + -4.5
x = 5.852349955 + -4.5

Combine like terms: 5.852349955 + -4.5 = 1.352349955
x = 1.352349955

Simplifying
x = 1.352349955


Subproblem 2
x + 4.5 = -5.852349955

Simplifying
x + 4.5 = -5.852349955

Reorder the terms:
4.5 + x = -5.852349955

Solving
4.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.852349955 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.852349955 + -4.5
x = -5.852349955 + -4.5

Combine like terms: -5.852349955 + -4.5 = -10.352349955
x = -10.352349955

Simplifying
x = -10.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.352349955, -10.352349955}
Solution
x = {1.352349955, -10.352349955}

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