x^2*7+19x+10=21

Solution for x^2*7+19x+10=21 equation:

Simplifying
x2 * 7 + 19x + 10 = 21

Reorder the terms for easier multiplication:
7x2 + 19x + 10 = 21

Reorder the terms:
10 + 19x + 7x2 = 21

Solving
10 + 19x + 7x2 = 21

Solving for variable 'x'.

Reorder the terms:
10 + -21 + 19x + 7x2 = 21 + -21

Combine like terms: 10 + -21 = -11
-11 + 19x + 7x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-11 + 19x + 7x2 = 0

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

Divide each side by '7'.
-1.571428571 + 2.714285714x + x2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 2.714285714x + 1.571428571 + x2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 2.714285714x + x2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 2.714285714x + x2 = 0 + 1.571428571
2.714285714x + x2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
2.714285714x + x2 = 1.571428571

The x term is 2.714285714x.  Take half its coefficient (1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
2.714285714x + 1.841836734 + x2 = 1.571428571 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714x + x2 = 1.571428571 + 1.841836734

Combine like terms: 1.571428571 + 1.841836734 = 3.413265305
1.841836734 + 2.714285714x + x2 = 3.413265305

Factor a perfect square on the left side:
(x + 1.357142857)(x + 1.357142857) = 3.413265305

Calculate the square root of the right side: 1.847502451

Break this problem into two subproblems by setting 
(x + 1.357142857) equal to 1.847502451 and -1.847502451.

Subproblem 1
x + 1.357142857 = 1.847502451

Simplifying
x + 1.357142857 = 1.847502451

Reorder the terms:
1.357142857 + x = 1.847502451

Solving
1.357142857 + x = 1.847502451

Solving for variable 'x'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + x = 1.847502451 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = 1.847502451 + -1.357142857
x = 1.847502451 + -1.357142857

Combine like terms: 1.847502451 + -1.357142857 = 0.490359594
x = 0.490359594

Simplifying
x = 0.490359594

Subproblem 2
x + 1.357142857 = -1.847502451

Simplifying
x + 1.357142857 = -1.847502451

Reorder the terms:
1.357142857 + x = -1.847502451

Solving
1.357142857 + x = -1.847502451

Solving for variable 'x'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + x = -1.847502451 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = -1.847502451 + -1.357142857
x = -1.847502451 + -1.357142857

Combine like terms: -1.847502451 + -1.357142857 = -3.204645308
x = -3.204645308

Simplifying
x = -3.204645308

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.490359594, -3.204645308}