7x^2+9x=1

Solution for 7x^2+9x=1 equation:

Simplifying
7x2 + 9x = 1

Reorder the terms:
9x + 7x2 = 1

Solving
9x + 7x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 9x + 7x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 9x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + 1.285714286x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 1.285714286x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 1.285714286x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 1.285714286x + x2 = 0 + 0.1428571429
1.285714286x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
1.285714286x + x2 = 0.1428571429

The x term is 1.285714286x.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286x + 0.4132653063 + x2 = 0.1428571429 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286x + x2 = 0.1428571429 + 0.4132653063

Combine like terms: 0.1428571429 + 0.4132653063 = 0.5561224492
0.4132653063 + 1.285714286x + x2 = 0.5561224492

Factor a perfect square on the left side:
(x + 0.642857143)(x + 0.642857143) = 0.5561224492

Calculate the square root of the right side: 0.745736179

Break this problem into two subproblems by setting 
(x + 0.642857143) equal to 0.745736179 and -0.745736179.

Subproblem 1
x + 0.642857143 = 0.745736179

Simplifying
x + 0.642857143 = 0.745736179

Reorder the terms:
0.642857143 + x = 0.745736179

Solving
0.642857143 + x = 0.745736179

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = 0.745736179 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = 0.745736179 + -0.642857143
x = 0.745736179 + -0.642857143

Combine like terms: 0.745736179 + -0.642857143 = 0.102879036
x = 0.102879036

Simplifying
x = 0.102879036

Subproblem 2
x + 0.642857143 = -0.745736179

Simplifying
x + 0.642857143 = -0.745736179

Reorder the terms:
0.642857143 + x = -0.745736179

Solving
0.642857143 + x = -0.745736179

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = -0.745736179 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = -0.745736179 + -0.642857143
x = -0.745736179 + -0.642857143

Combine like terms: -0.745736179 + -0.642857143 = -1.388593322
x = -1.388593322

Simplifying
x = -1.388593322

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.102879036, -1.388593322}