7x^2+19x+10=19.42

Solution for 7x^2+19x+10=19.42 equation:

Simplifying
7x2 + 19x + 10 = 19.42

Reorder the terms:
10 + 19x + 7x2 = 19.42

Solving
10 + 19x + 7x2 = 19.42

Solving for variable 'x'.

Reorder the terms:
10 + -19.42 + 19x + 7x2 = 19.42 + -19.42

Combine like terms: 10 + -19.42 = -9.42
-9.42 + 19x + 7x2 = 19.42 + -19.42

Combine like terms: 19.42 + -19.42 = 0.00
-9.42 + 19x + 7x2 = 0.00

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

Divide each side by '7'.
-1.345714286 + 2.714285714x + x2 = 0.00

Move the constant term to the right:

Add '1.345714286' to each side of the equation.
-1.345714286 + 2.714285714x + 1.345714286 + x2 = 0.00 + 1.345714286

Reorder the terms:
-1.345714286 + 1.345714286 + 2.714285714x + x2 = 0.00 + 1.345714286

Combine like terms: -1.345714286 + 1.345714286 = 0.000000000
0.000000000 + 2.714285714x + x2 = 0.00 + 1.345714286
2.714285714x + x2 = 0.00 + 1.345714286

Combine like terms: 0.00 + 1.345714286 = 1.345714286
2.714285714x + x2 = 1.345714286

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 = 1.345714286 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714x + x2 = 1.345714286 + 1.841836734

Combine like terms: 1.345714286 + 1.841836734 = 3.18755102
1.841836734 + 2.714285714x + x2 = 3.18755102

Factor a perfect square on the left side:
(x + 1.357142857)(x + 1.357142857) = 3.18755102

Calculate the square root of the right side: 1.785371396

Break this problem into two subproblems by setting 
(x + 1.357142857) equal to 1.785371396 and -1.785371396.

Subproblem 1
x + 1.357142857 = 1.785371396

Simplifying
x + 1.357142857 = 1.785371396

Reorder the terms:
1.357142857 + x = 1.785371396

Solving
1.357142857 + x = 1.785371396

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 = 1.785371396 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = 1.785371396 + -1.357142857
x = 1.785371396 + -1.357142857

Combine like terms: 1.785371396 + -1.357142857 = 0.428228539
x = 0.428228539

Simplifying
x = 0.428228539

Subproblem 2
x + 1.357142857 = -1.785371396

Simplifying
x + 1.357142857 = -1.785371396

Reorder the terms:
1.357142857 + x = -1.785371396

Solving
1.357142857 + x = -1.785371396

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 = -1.785371396 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = -1.785371396 + -1.357142857
x = -1.785371396 + -1.357142857

Combine like terms: -1.785371396 + -1.357142857 = -3.142514253
x = -3.142514253

Simplifying
x = -3.142514253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.428228539, -3.142514253}