6x^2-35x+48=0

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Solution for 6x^2-35x+48=0 equation: 


Simplifying
6x2 + -35x + 48 = 0

Reorder the terms:
48 + -35x + 6x2 = 0

Solving
48 + -35x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
8 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -5.833333333x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -5.833333333x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5.833333333x + x2 = 0 + -8
-5.833333333x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-5.833333333x + x2 = -8

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = -8 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = -8 + 8.506944446

Combine like terms: -8 + 8.506944446 = 0.506944446
8.506944446 + -5.833333333x + x2 = 0.506944446

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 0.506944446

Calculate the square root of the right side: 0.712000313

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 0.712000313 and -0.712000313.


Subproblem 1
x + -2.916666667 = 0.712000313

Simplifying
x + -2.916666667 = 0.712000313

Reorder the terms:
-2.916666667 + x = 0.712000313

Solving
-2.916666667 + x = 0.712000313

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = 0.712000313 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = 0.712000313 + 2.916666667
x = 0.712000313 + 2.916666667

Combine like terms: 0.712000313 + 2.916666667 = 3.62866698
x = 3.62866698

Simplifying
x = 3.62866698


Subproblem 2
x + -2.916666667 = -0.712000313

Simplifying
x + -2.916666667 = -0.712000313

Reorder the terms:
-2.916666667 + x = -0.712000313

Solving
-2.916666667 + x = -0.712000313

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = -0.712000313 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = -0.712000313 + 2.916666667
x = -0.712000313 + 2.916666667

Combine like terms: -0.712000313 + 2.916666667 = 2.204666354
x = 2.204666354

Simplifying
x = 2.204666354


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.62866698, 2.204666354}

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