4x^2+2x+3=10

Solution for 4x^2+2x+3=10 equation:

Simplifying
4x2 + 2x + 3 = 10

Reorder the terms:
3 + 2x + 4x2 = 10

Solving
3 + 2x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
3 + -10 + 2x + 4x2 = 10 + -10

Combine like terms: 3 + -10 = -7
-7 + 2x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-7 + 2x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 0.5x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 0.5x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 0.5x + x2 = 0 + 1.75
0.5x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
0.5x + x2 = 1.75

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.75 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.75 + 0.0625

Combine like terms: 1.75 + 0.0625 = 1.8125
0.0625 + 0.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.346291202 and -1.346291202.

Subproblem 1
x + 0.25 = 1.346291202

Simplifying
x + 0.25 = 1.346291202

Reorder the terms:
0.25 + x = 1.346291202

Solving
0.25 + x = 1.346291202

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.346291202 + -0.25
x = 1.346291202 + -0.25

Combine like terms: 1.346291202 + -0.25 = 1.096291202
x = 1.096291202

Simplifying
x = 1.096291202

Subproblem 2
x + 0.25 = -1.346291202

Simplifying
x + 0.25 = -1.346291202

Reorder the terms:
0.25 + x = -1.346291202

Solving
0.25 + x = -1.346291202

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.346291202 + -0.25
x = -1.346291202 + -0.25

Combine like terms: -1.346291202 + -0.25 = -1.596291202
x = -1.596291202

Simplifying
x = -1.596291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.096291202, -1.596291202}