23x^2+50x+25=0

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Solution for 23x^2+50x+25=0 equation: 


Simplifying
23x2 + 50x + 25 = 0

Reorder the terms:
25 + 50x + 23x2 = 0

Solving
25 + 50x + 23x2 = 0

Solving for variable 'x'.

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

Divide each side by '23'.
1.086956522 + 2.173913043x + x2 = 0

Move the constant term to the right:

Add '-1.086956522' to each side of the equation.
1.086956522 + 2.173913043x + -1.086956522 + x2 = 0 + -1.086956522

Reorder the terms:
1.086956522 + -1.086956522 + 2.173913043x + x2 = 0 + -1.086956522

Combine like terms: 1.086956522 + -1.086956522 = 0.000000000
0.000000000 + 2.173913043x + x2 = 0 + -1.086956522
2.173913043x + x2 = 0 + -1.086956522

Combine like terms: 0 + -1.086956522 = -1.086956522
2.173913043x + x2 = -1.086956522

The x term is 2.173913043x.  Take half its coefficient (1.086956522).
Square it (1.181474481) and add it to both sides.

Add '1.181474481' to each side of the equation.
2.173913043x + 1.181474481 + x2 = -1.086956522 + 1.181474481

Reorder the terms:
1.181474481 + 2.173913043x + x2 = -1.086956522 + 1.181474481

Combine like terms: -1.086956522 + 1.181474481 = 0.094517959
1.181474481 + 2.173913043x + x2 = 0.094517959

Factor a perfect square on the left side:
(x + 1.086956522)(x + 1.086956522) = 0.094517959

Calculate the square root of the right side: 0.307437732

Break this problem into two subproblems by setting 
(x + 1.086956522) equal to 0.307437732 and -0.307437732.


Subproblem 1
x + 1.086956522 = 0.307437732

Simplifying
x + 1.086956522 = 0.307437732

Reorder the terms:
1.086956522 + x = 0.307437732

Solving
1.086956522 + x = 0.307437732

Solving for variable 'x'.

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

Add '-1.086956522' to each side of the equation.
1.086956522 + -1.086956522 + x = 0.307437732 + -1.086956522

Combine like terms: 1.086956522 + -1.086956522 = 0.000000000
0.000000000 + x = 0.307437732 + -1.086956522
x = 0.307437732 + -1.086956522

Combine like terms: 0.307437732 + -1.086956522 = -0.77951879
x = -0.77951879

Simplifying
x = -0.77951879


Subproblem 2
x + 1.086956522 = -0.307437732

Simplifying
x + 1.086956522 = -0.307437732

Reorder the terms:
1.086956522 + x = -0.307437732

Solving
1.086956522 + x = -0.307437732

Solving for variable 'x'.

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

Add '-1.086956522' to each side of the equation.
1.086956522 + -1.086956522 + x = -0.307437732 + -1.086956522

Combine like terms: 1.086956522 + -1.086956522 = 0.000000000
0.000000000 + x = -0.307437732 + -1.086956522
x = -0.307437732 + -1.086956522

Combine like terms: -0.307437732 + -1.086956522 = -1.394394254
x = -1.394394254

Simplifying
x = -1.394394254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.77951879, -1.394394254}

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