58x^2-35x-4=0

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Solution for 58x^2-35x-4=0 equation: 


Simplifying
58x2 + -35x + -4 = 0

Reorder the terms:
-4 + -35x + 58x2 = 0

Solving
-4 + -35x + 58x2 = 0

Solving for variable 'x'.

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

Divide each side by '58'.
-0.06896551724 + -0.6034482759x + x2 = 0

Move the constant term to the right:

Add '0.06896551724' to each side of the equation.
-0.06896551724 + -0.6034482759x + 0.06896551724 + x2 = 0 + 0.06896551724

Reorder the terms:
-0.06896551724 + 0.06896551724 + -0.6034482759x + x2 = 0 + 0.06896551724

Combine like terms: -0.06896551724 + 0.06896551724 = 0.00000000000
0.00000000000 + -0.6034482759x + x2 = 0 + 0.06896551724
-0.6034482759x + x2 = 0 + 0.06896551724

Combine like terms: 0 + 0.06896551724 = 0.06896551724
-0.6034482759x + x2 = 0.06896551724

The x term is -0.6034482759x.  Take half its coefficient (-0.301724138).
Square it (0.09103745545) and add it to both sides.

Add '0.09103745545' to each side of the equation.
-0.6034482759x + 0.09103745545 + x2 = 0.06896551724 + 0.09103745545

Reorder the terms:
0.09103745545 + -0.6034482759x + x2 = 0.06896551724 + 0.09103745545

Combine like terms: 0.06896551724 + 0.09103745545 = 0.16000297269
0.09103745545 + -0.6034482759x + x2 = 0.16000297269

Factor a perfect square on the left side:
(x + -0.301724138)(x + -0.301724138) = 0.16000297269

Calculate the square root of the right side: 0.400003716

Break this problem into two subproblems by setting 
(x + -0.301724138) equal to 0.400003716 and -0.400003716.


Subproblem 1
x + -0.301724138 = 0.400003716

Simplifying
x + -0.301724138 = 0.400003716

Reorder the terms:
-0.301724138 + x = 0.400003716

Solving
-0.301724138 + x = 0.400003716

Solving for variable 'x'.

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

Add '0.301724138' to each side of the equation.
-0.301724138 + 0.301724138 + x = 0.400003716 + 0.301724138

Combine like terms: -0.301724138 + 0.301724138 = 0.000000000
0.000000000 + x = 0.400003716 + 0.301724138
x = 0.400003716 + 0.301724138

Combine like terms: 0.400003716 + 0.301724138 = 0.701727854
x = 0.701727854

Simplifying
x = 0.701727854


Subproblem 2
x + -0.301724138 = -0.400003716

Simplifying
x + -0.301724138 = -0.400003716

Reorder the terms:
-0.301724138 + x = -0.400003716

Solving
-0.301724138 + x = -0.400003716

Solving for variable 'x'.

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

Add '0.301724138' to each side of the equation.
-0.301724138 + 0.301724138 + x = -0.400003716 + 0.301724138

Combine like terms: -0.301724138 + 0.301724138 = 0.000000000
0.000000000 + x = -0.400003716 + 0.301724138
x = -0.400003716 + 0.301724138

Combine like terms: -0.400003716 + 0.301724138 = -0.098279578
x = -0.098279578

Simplifying
x = -0.098279578


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701727854, -0.098279578}

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