16x^2-24x-241=0

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Solution for 16x^2-24x-241=0 equation: 


Simplifying
16x2 + -24x + -241 = 0

Reorder the terms:
-241 + -24x + 16x2 = 0

Solving
-241 + -24x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-15.0625 + -1.5x + x2 = 0

Move the constant term to the right:

Add '15.0625' to each side of the equation.
-15.0625 + -1.5x + 15.0625 + x2 = 0 + 15.0625

Reorder the terms:
-15.0625 + 15.0625 + -1.5x + x2 = 0 + 15.0625

Combine like terms: -15.0625 + 15.0625 = 0.0000
0.0000 + -1.5x + x2 = 0 + 15.0625
-1.5x + x2 = 0 + 15.0625

Combine like terms: 0 + 15.0625 = 15.0625
-1.5x + x2 = 15.0625

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 = 15.0625 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 15.0625 + 0.5625

Combine like terms: 15.0625 + 0.5625 = 15.625
0.5625 + -1.5x + x2 = 15.625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 15.625

Calculate the square root of the right side: 3.952847075

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.952847075 and -3.952847075.


Subproblem 1
x + -0.75 = 3.952847075

Simplifying
x + -0.75 = 3.952847075

Reorder the terms:
-0.75 + x = 3.952847075

Solving
-0.75 + x = 3.952847075

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 = 3.952847075 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.952847075 + 0.75
x = 3.952847075 + 0.75

Combine like terms: 3.952847075 + 0.75 = 4.702847075
x = 4.702847075

Simplifying
x = 4.702847075


Subproblem 2
x + -0.75 = -3.952847075

Simplifying
x + -0.75 = -3.952847075

Reorder the terms:
-0.75 + x = -3.952847075

Solving
-0.75 + x = -3.952847075

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 = -3.952847075 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.952847075 + 0.75
x = -3.952847075 + 0.75

Combine like terms: -3.952847075 + 0.75 = -3.202847075
x = -3.202847075

Simplifying
x = -3.202847075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.702847075, -3.202847075}

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