234x-(235-23434x^2)=345

Solution for 234x-(235-23434x^2)=345 equation:

Simplifying
234x + -1(235 + -23434x2) = 345
234x + (235 * -1 + -23434x2 * -1) = 345
234x + (-235 + 23434x2) = 345

Reorder the terms:
-235 + 234x + 23434x2 = 345

Solving
-235 + 234x + 23434x2 = 345

Solving for variable 'x'.

Reorder the terms:
-235 + -345 + 234x + 23434x2 = 345 + -345

Combine like terms: -235 + -345 = -580
-580 + 234x + 23434x2 = 345 + -345

Combine like terms: 345 + -345 = 0
-580 + 234x + 23434x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-290 + 117x + 11717x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-290 + 117x + 11717x2)' equal to zero and attempt to solve:

Simplifying
-290 + 117x + 11717x2 = 0

Solving
-290 + 117x + 11717x2 = 0

Begin completing the square.  Divide all terms by
11717 the coefficient of the squared term: 

Divide each side by '11717'.
-0.02475036272 + 0.009985491167x + x2 = 0

Move the constant term to the right:

Add '0.02475036272' to each side of the equation.
-0.02475036272 + 0.009985491167x + 0.02475036272 + x2 = 0 + 0.02475036272

Reorder the terms:
-0.02475036272 + 0.02475036272 + 0.009985491167x + x2 = 0 + 0.02475036272

Combine like terms: -0.02475036272 + 0.02475036272 = 0.00000000000
0.00000000000 + 0.009985491167x + x2 = 0 + 0.02475036272
0.009985491167x + x2 = 0 + 0.02475036272

Combine like terms: 0 + 0.02475036272 = 0.02475036272
0.009985491167x + x2 = 0.02475036272

The x term is 0.009985491167x.  Take half its coefficient (0.004992745584).
Square it (0.00002492750847) and add it to both sides.

Add '0.00002492750847' to each side of the equation.
0.009985491167x + 0.00002492750847 + x2 = 0.02475036272 + 0.00002492750847

Reorder the terms:
0.00002492750847 + 0.009985491167x + x2 = 0.02475036272 + 0.00002492750847

Combine like terms: 0.02475036272 + 0.00002492750847 = 0.02477529022847
0.00002492750847 + 0.009985491167x + x2 = 0.02477529022847

Factor a perfect square on the left side:
(x + 0.004992745584)(x + 0.004992745584) = 0.02477529022847

Calculate the square root of the right side: 0.157401684

Break this problem into two subproblems by setting 
(x + 0.004992745584) equal to 0.157401684 and -0.157401684.

Subproblem 1
x + 0.004992745584 = 0.157401684

Simplifying
x + 0.004992745584 = 0.157401684

Reorder the terms:
0.004992745584 + x = 0.157401684

Solving
0.004992745584 + x = 0.157401684

Solving for variable 'x'.

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

Add '-0.004992745584' to each side of the equation.
0.004992745584 + -0.004992745584 + x = 0.157401684 + -0.004992745584

Combine like terms: 0.004992745584 + -0.004992745584 = 0.000000000000
0.000000000000 + x = 0.157401684 + -0.004992745584
x = 0.157401684 + -0.004992745584

Combine like terms: 0.157401684 + -0.004992745584 = 0.152408938416
x = 0.152408938416

Simplifying
x = 0.152408938416

Subproblem 2
x + 0.004992745584 = -0.157401684

Simplifying
x + 0.004992745584 = -0.157401684

Reorder the terms:
0.004992745584 + x = -0.157401684

Solving
0.004992745584 + x = -0.157401684

Solving for variable 'x'.

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

Add '-0.004992745584' to each side of the equation.
0.004992745584 + -0.004992745584 + x = -0.157401684 + -0.004992745584

Combine like terms: 0.004992745584 + -0.004992745584 = 0.000000000000
0.000000000000 + x = -0.157401684 + -0.004992745584
x = -0.157401684 + -0.004992745584

Combine like terms: -0.157401684 + -0.004992745584 = -0.162394429584
x = -0.162394429584

Simplifying
x = -0.162394429584

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.152408938416, -0.162394429584}
Solution
x = {0.152408938416, -0.162394429584}