2x^2-11x-48=0

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Solution for 2x^2-11x-48=0 equation: 


Simplifying
2x2 + -11x + -48 = 0

Reorder the terms:
-48 + -11x + 2x2 = 0

Solving
-48 + -11x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-24 + -5.5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -5.5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -5.5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -5.5x + x2 = 0 + 24
-5.5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-5.5x + x2 = 24

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 24 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 24 + 7.5625

Combine like terms: 24 + 7.5625 = 31.5625
7.5625 + -5.5x + x2 = 31.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(x + -2.75) equal to 5.618051264 and -5.618051264.


Subproblem 1
x + -2.75 = 5.618051264

Simplifying
x + -2.75 = 5.618051264

Reorder the terms:
-2.75 + x = 5.618051264

Solving
-2.75 + x = 5.618051264

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 5.618051264 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 5.618051264 + 2.75
x = 5.618051264 + 2.75

Combine like terms: 5.618051264 + 2.75 = 8.368051264
x = 8.368051264

Simplifying
x = 8.368051264


Subproblem 2
x + -2.75 = -5.618051264

Simplifying
x + -2.75 = -5.618051264

Reorder the terms:
-2.75 + x = -5.618051264

Solving
-2.75 + x = -5.618051264

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -5.618051264 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -5.618051264 + 2.75
x = -5.618051264 + 2.75

Combine like terms: -5.618051264 + 2.75 = -2.868051264
x = -2.868051264

Simplifying
x = -2.868051264


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.368051264, -2.868051264}

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