48x^2-300x+102=0

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Solution for 48x^2-300x+102=0 equation: 


Simplifying
48x2 + -300x + 102 = 0

Reorder the terms:
102 + -300x + 48x2 = 0

Solving
102 + -300x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(17 + -50x + 8x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(17 + -50x + 8x2)' equal to zero and attempt to solve:

Simplifying
17 + -50x + 8x2 = 0

Solving
17 + -50x + 8x2 = 0

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

Divide each side by '8'.
2.125 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + -6.25x + -2.125 + x2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + -6.25x + x2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + -6.25x + x2 = 0 + -2.125
-6.25x + x2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
-6.25x + x2 = -2.125

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -2.125 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -2.125 + 9.765625

Combine like terms: -2.125 + 9.765625 = 7.640625
9.765625 + -6.25x + x2 = 7.640625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 7.640625

Calculate the square root of the right side: 2.764168048

Break this problem into two subproblems by setting 
(x + -3.125) equal to 2.764168048 and -2.764168048.


Subproblem 1
x + -3.125 = 2.764168048

Simplifying
x + -3.125 = 2.764168048

Reorder the terms:
-3.125 + x = 2.764168048

Solving
-3.125 + x = 2.764168048

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 2.764168048 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 2.764168048 + 3.125
x = 2.764168048 + 3.125

Combine like terms: 2.764168048 + 3.125 = 5.889168048
x = 5.889168048

Simplifying
x = 5.889168048


Subproblem 2
x + -3.125 = -2.764168048

Simplifying
x + -3.125 = -2.764168048

Reorder the terms:
-3.125 + x = -2.764168048

Solving
-3.125 + x = -2.764168048

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -2.764168048 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -2.764168048 + 3.125
x = -2.764168048 + 3.125

Combine like terms: -2.764168048 + 3.125 = 0.360831952
x = 0.360831952

Simplifying
x = 0.360831952


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.889168048, 0.360831952}
Solution
x = {5.889168048, 0.360831952}

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