6+4*x+(x^2)*5=23

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Solution for 6+4*x+(x^2)*5=23 equation: 


Simplifying
6 + 4x + (x2) * 5 = 23

Reorder the terms for easier multiplication:
6 + 4x + 5x2 = 23

Solving
6 + 4x + 5x2 = 23

Solving for variable 'x'.

Reorder the terms:
6 + -23 + 4x + 5x2 = 23 + -23

Combine like terms: 6 + -23 = -17
-17 + 4x + 5x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-17 + 4x + 5x2 = 0

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

Divide each side by '5'.
-3.4 + 0.8x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + 0.8x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + 0.8x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + 0.8x + x2 = 0 + 3.4
0.8x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
0.8x + x2 = 3.4

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 3.4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 3.4 + 0.16

Combine like terms: 3.4 + 0.16 = 3.56
0.16 + 0.8x + x2 = 3.56

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.886796226 and -1.886796226.


Subproblem 1
x + 0.4 = 1.886796226

Simplifying
x + 0.4 = 1.886796226

Reorder the terms:
0.4 + x = 1.886796226

Solving
0.4 + x = 1.886796226

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.886796226 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.886796226 + -0.4
x = 1.886796226 + -0.4

Combine like terms: 1.886796226 + -0.4 = 1.486796226
x = 1.486796226

Simplifying
x = 1.486796226


Subproblem 2
x + 0.4 = -1.886796226

Simplifying
x + 0.4 = -1.886796226

Reorder the terms:
0.4 + x = -1.886796226

Solving
0.4 + x = -1.886796226

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.886796226 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.886796226 + -0.4
x = -1.886796226 + -0.4

Combine like terms: -1.886796226 + -0.4 = -2.286796226
x = -2.286796226

Simplifying
x = -2.286796226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.486796226, -2.286796226}

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