10x^2+2x-5814=0

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Solution for 10x^2+2x-5814=0 equation: 


Simplifying
10x2 + 2x + -5814 = 0

Reorder the terms:
-5814 + 2x + 10x2 = 0

Solving
-5814 + 2x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2907 + x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2907 + x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2907 + x + 5x2 = 0

Solving
-2907 + x + 5x2 = 0

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

Divide each side by '5'.
-581.4 + 0.2x + x2 = 0

Move the constant term to the right:

Add '581.4' to each side of the equation.
-581.4 + 0.2x + 581.4 + x2 = 0 + 581.4

Reorder the terms:
-581.4 + 581.4 + 0.2x + x2 = 0 + 581.4

Combine like terms: -581.4 + 581.4 = 0.0
0.0 + 0.2x + x2 = 0 + 581.4
0.2x + x2 = 0 + 581.4

Combine like terms: 0 + 581.4 = 581.4
0.2x + x2 = 581.4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2x + 0.25 + x2 = 581.4 + 0.25

Reorder the terms:
0.25 + 0.2x + x2 = 581.4 + 0.25

Combine like terms: 581.4 + 0.25 = 581.65
0.25 + 0.2x + x2 = 581.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 581.65

Calculate the square root of the right side: 24.117421089

Break this problem into two subproblems by setting 
(x + 0.5) equal to 24.117421089 and -24.117421089.


Subproblem 1
x + 0.5 = 24.117421089

Simplifying
x + 0.5 = 24.117421089

Reorder the terms:
0.5 + x = 24.117421089

Solving
0.5 + x = 24.117421089

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 24.117421089 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 24.117421089 + -0.5
x = 24.117421089 + -0.5

Combine like terms: 24.117421089 + -0.5 = 23.617421089
x = 23.617421089

Simplifying
x = 23.617421089


Subproblem 2
x + 0.5 = -24.117421089

Simplifying
x + 0.5 = -24.117421089

Reorder the terms:
0.5 + x = -24.117421089

Solving
0.5 + x = -24.117421089

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -24.117421089 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -24.117421089 + -0.5
x = -24.117421089 + -0.5

Combine like terms: -24.117421089 + -0.5 = -24.617421089
x = -24.617421089

Simplifying
x = -24.617421089


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.617421089, -24.617421089}
Solution
x = {23.617421089, -24.617421089}

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