10x^2+10x+3=19-4x^2+16

Solution for 10x^2+10x+3=19-4x^2+16 equation:

Simplifying
10x2 + 10x + 3 = 19 + -4x2 + 16

Reorder the terms:
3 + 10x + 10x2 = 19 + -4x2 + 16

Reorder the terms:
3 + 10x + 10x2 = 19 + 16 + -4x2

Combine like terms: 19 + 16 = 35
3 + 10x + 10x2 = 35 + -4x2

Solving
3 + 10x + 10x2 = 35 + -4x2

Solving for variable 'x'.

Reorder the terms:
3 + -35 + 10x + 10x2 + 4x2 = 35 + -4x2 + -35 + 4x2

Combine like terms: 3 + -35 = -32
-32 + 10x + 10x2 + 4x2 = 35 + -4x2 + -35 + 4x2

Combine like terms: 10x2 + 4x2 = 14x2
-32 + 10x + 14x2 = 35 + -4x2 + -35 + 4x2

Reorder the terms:
-32 + 10x + 14x2 = 35 + -35 + -4x2 + 4x2

Combine like terms: 35 + -35 = 0
-32 + 10x + 14x2 = 0 + -4x2 + 4x2
-32 + 10x + 14x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-32 + 10x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 5x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + 5x + 7x2)' equal to zero and attempt to solve:

Simplifying
-16 + 5x + 7x2 = 0

Solving
-16 + 5x + 7x2 = 0

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

Divide each side by '7'.
-2.285714286 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 0.7142857143x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 0.7142857143x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 0.7142857143x + x2 = 0 + 2.285714286
0.7142857143x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
0.7142857143x + x2 = 2.285714286

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 2.285714286 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 2.285714286 + 0.1275510204

Combine like terms: 2.285714286 + 0.1275510204 = 2.4132653064
0.1275510204 + 0.7142857143x + x2 = 2.4132653064

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 2.4132653064

Calculate the square root of the right side: 1.553468798

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 1.553468798 and -1.553468798.

Subproblem 1
x + 0.3571428572 = 1.553468798

Simplifying
x + 0.3571428572 = 1.553468798

Reorder the terms:
0.3571428572 + x = 1.553468798

Solving
0.3571428572 + x = 1.553468798

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = 1.553468798 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = 1.553468798 + -0.3571428572
x = 1.553468798 + -0.3571428572

Combine like terms: 1.553468798 + -0.3571428572 = 1.1963259408
x = 1.1963259408

Simplifying
x = 1.1963259408

Subproblem 2
x + 0.3571428572 = -1.553468798

Simplifying
x + 0.3571428572 = -1.553468798

Reorder the terms:
0.3571428572 + x = -1.553468798

Solving
0.3571428572 + x = -1.553468798

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = -1.553468798 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = -1.553468798 + -0.3571428572
x = -1.553468798 + -0.3571428572

Combine like terms: -1.553468798 + -0.3571428572 = -1.9106116552
x = -1.9106116552

Simplifying
x = -1.9106116552

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1963259408, -1.9106116552}
Solution
x = {1.1963259408, -1.9106116552}