16x^2-24x+9=44

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Solution for 16x^2-24x+9=44 equation: 


Simplifying
16x2 + -24x + 9 = 44

Reorder the terms:
9 + -24x + 16x2 = 44

Solving
9 + -24x + 16x2 = 44

Solving for variable 'x'.

Reorder the terms:
9 + -44 + -24x + 16x2 = 44 + -44

Combine like terms: 9 + -44 = -35
-35 + -24x + 16x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-35 + -24x + 16x2 = 0

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

Divide each side by '16'.
-2.1875 + -1.5x + x2 = 0

Move the constant term to the right:

Add '2.1875' to each side of the equation.
-2.1875 + -1.5x + 2.1875 + x2 = 0 + 2.1875

Reorder the terms:
-2.1875 + 2.1875 + -1.5x + x2 = 0 + 2.1875

Combine like terms: -2.1875 + 2.1875 = 0.0000
0.0000 + -1.5x + x2 = 0 + 2.1875
-1.5x + x2 = 0 + 2.1875

Combine like terms: 0 + 2.1875 = 2.1875
-1.5x + x2 = 2.1875

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 2.1875 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 2.1875 + 0.5625

Combine like terms: 2.1875 + 0.5625 = 2.75
0.5625 + -1.5x + x2 = 2.75

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + -0.75 = 1.658312395

Simplifying
x + -0.75 = 1.658312395

Reorder the terms:
-0.75 + x = 1.658312395

Solving
-0.75 + x = 1.658312395

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.658312395 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.658312395 + 0.75
x = 1.658312395 + 0.75

Combine like terms: 1.658312395 + 0.75 = 2.408312395
x = 2.408312395

Simplifying
x = 2.408312395


Subproblem 2
x + -0.75 = -1.658312395

Simplifying
x + -0.75 = -1.658312395

Reorder the terms:
-0.75 + x = -1.658312395

Solving
-0.75 + x = -1.658312395

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.658312395 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.658312395 + 0.75
x = -1.658312395 + 0.75

Combine like terms: -1.658312395 + 0.75 = -0.908312395
x = -0.908312395

Simplifying
x = -0.908312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.408312395, -0.908312395}

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