74x^2-47x*(18x-9)+2=58

Solution for 74x^2-47x*(18x-9)+2=58 equation:

Simplifying
74x2 + -47x(18x + -9) + 2 = 58

Reorder the terms:
74x2 + -47x(-9 + 18x) + 2 = 58
74x2 + (-9 * -47x + 18x * -47x) + 2 = 58
74x2 + (423x + -846x2) + 2 = 58

Reorder the terms:
2 + 423x + 74x2 + -846x2 = 58

Combine like terms: 74x2 + -846x2 = -772x2
2 + 423x + -772x2 = 58

Solving
2 + 423x + -772x2 = 58

Solving for variable 'x'.

Reorder the terms:
2 + -58 + 423x + -772x2 = 58 + -58

Combine like terms: 2 + -58 = -56
-56 + 423x + -772x2 = 58 + -58

Combine like terms: 58 + -58 = 0
-56 + 423x + -772x2 = 0

Begin completing the square.  Divide all terms by
-772 the coefficient of the squared term: 

Divide each side by '-772'.
0.0725388601 + -0.5479274611x + x2 = 0

Move the constant term to the right:

Add '-0.0725388601' to each side of the equation.
0.0725388601 + -0.5479274611x + -0.0725388601 + x2 = 0 + -0.0725388601

Reorder the terms:
0.0725388601 + -0.0725388601 + -0.5479274611x + x2 = 0 + -0.0725388601

Combine like terms: 0.0725388601 + -0.0725388601 = 0.0000000000
0.0000000000 + -0.5479274611x + x2 = 0 + -0.0725388601
-0.5479274611x + x2 = 0 + -0.0725388601

Combine like terms: 0 + -0.0725388601 = -0.0725388601
-0.5479274611x + x2 = -0.0725388601

The x term is -0.5479274611x.  Take half its coefficient (-0.2739637306).
Square it (0.07505612568) and add it to both sides.

Add '0.07505612568' to each side of the equation.
-0.5479274611x + 0.07505612568 + x2 = -0.0725388601 + 0.07505612568

Reorder the terms:
0.07505612568 + -0.5479274611x + x2 = -0.0725388601 + 0.07505612568

Combine like terms: -0.0725388601 + 0.07505612568 = 0.00251726558
0.07505612568 + -0.5479274611x + x2 = 0.00251726558

Factor a perfect square on the left side:
(x + -0.2739637306)(x + -0.2739637306) = 0.00251726558

Calculate the square root of the right side: 0.050172359

Break this problem into two subproblems by setting 
(x + -0.2739637306) equal to 0.050172359 and -0.050172359.

Subproblem 1
x + -0.2739637306 = 0.050172359

Simplifying
x + -0.2739637306 = 0.050172359

Reorder the terms:
-0.2739637306 + x = 0.050172359

Solving
-0.2739637306 + x = 0.050172359

Solving for variable 'x'.

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

Add '0.2739637306' to each side of the equation.
-0.2739637306 + 0.2739637306 + x = 0.050172359 + 0.2739637306

Combine like terms: -0.2739637306 + 0.2739637306 = 0.0000000000
0.0000000000 + x = 0.050172359 + 0.2739637306
x = 0.050172359 + 0.2739637306

Combine like terms: 0.050172359 + 0.2739637306 = 0.3241360896
x = 0.3241360896

Simplifying
x = 0.3241360896

Subproblem 2
x + -0.2739637306 = -0.050172359

Simplifying
x + -0.2739637306 = -0.050172359

Reorder the terms:
-0.2739637306 + x = -0.050172359

Solving
-0.2739637306 + x = -0.050172359

Solving for variable 'x'.

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

Add '0.2739637306' to each side of the equation.
-0.2739637306 + 0.2739637306 + x = -0.050172359 + 0.2739637306

Combine like terms: -0.2739637306 + 0.2739637306 = 0.0000000000
0.0000000000 + x = -0.050172359 + 0.2739637306
x = -0.050172359 + 0.2739637306

Combine like terms: -0.050172359 + 0.2739637306 = 0.2237913716
x = 0.2237913716

Simplifying
x = 0.2237913716

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3241360896, 0.2237913716}