25x^2-100x-48=0

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Solution for 25x^2-100x-48=0 equation: 


Simplifying
25x2 + -100x + -48 = 0

Reorder the terms:
-48 + -100x + 25x2 = 0

Solving
-48 + -100x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-1.92 + -4x + x2 = 0

Move the constant term to the right:

Add '1.92' to each side of the equation.
-1.92 + -4x + 1.92 + x2 = 0 + 1.92

Reorder the terms:
-1.92 + 1.92 + -4x + x2 = 0 + 1.92

Combine like terms: -1.92 + 1.92 = 0.00
0.00 + -4x + x2 = 0 + 1.92
-4x + x2 = 0 + 1.92

Combine like terms: 0 + 1.92 = 1.92
-4x + x2 = 1.92

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 = 1.92 + 4

Reorder the terms:
4 + -4x + x2 = 1.92 + 4

Combine like terms: 1.92 + 4 = 5.92
4 + -4x + x2 = 5.92

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.92

Calculate the square root of the right side: 2.433105012

Break this problem into two subproblems by setting 
(x + -2) equal to 2.433105012 and -2.433105012.


Subproblem 1
x + -2 = 2.433105012

Simplifying
x + -2 = 2.433105012

Reorder the terms:
-2 + x = 2.433105012

Solving
-2 + x = 2.433105012

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 = 2.433105012 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.433105012 + 2
x = 2.433105012 + 2

Combine like terms: 2.433105012 + 2 = 4.433105012
x = 4.433105012

Simplifying
x = 4.433105012


Subproblem 2
x + -2 = -2.433105012

Simplifying
x + -2 = -2.433105012

Reorder the terms:
-2 + x = -2.433105012

Solving
-2 + x = -2.433105012

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 = -2.433105012 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.433105012 + 2
x = -2.433105012 + 2

Combine like terms: -2.433105012 + 2 = -0.433105012
x = -0.433105012

Simplifying
x = -0.433105012


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.433105012, -0.433105012}

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