0.81x^2+70x=1

Solution for 0.81x^2+70x=1 equation:

Simplifying
0.81x2 + 70x = 1

Reorder the terms:
70x + 0.81x2 = 1

Solving
70x + 0.81x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 70x + 0.81x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 70x + 0.81x2 = 0

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

Divide each side by '0.81'.
-1.234567901 + 86.41975309x + x2 = 0

Move the constant term to the right:

Add '1.234567901' to each side of the equation.
-1.234567901 + 86.41975309x + 1.234567901 + x2 = 0 + 1.234567901

Reorder the terms:
-1.234567901 + 1.234567901 + 86.41975309x + x2 = 0 + 1.234567901

Combine like terms: -1.234567901 + 1.234567901 = 0.000000000
0.000000000 + 86.41975309x + x2 = 0 + 1.234567901
86.41975309x + x2 = 0 + 1.234567901

Combine like terms: 0 + 1.234567901 = 1.234567901
86.41975309x + x2 = 1.234567901

The x term is 86.41975309x.  Take half its coefficient (43.20987655).
Square it (1867.093431) and add it to both sides.

Add '1867.093431' to each side of the equation.
86.41975309x + 1867.093431 + x2 = 1.234567901 + 1867.093431

Reorder the terms:
1867.093431 + 86.41975309x + x2 = 1.234567901 + 1867.093431

Combine like terms: 1.234567901 + 1867.093431 = 1868.327998901
1867.093431 + 86.41975309x + x2 = 1868.327998901

Factor a perfect square on the left side:
(x + 43.20987655)(x + 43.20987655) = 1868.327998901

Calculate the square root of the right side: 43.224159898

Break this problem into two subproblems by setting 
(x + 43.20987655) equal to 43.224159898 and -43.224159898.

Subproblem 1
x + 43.20987655 = 43.224159898

Simplifying
x + 43.20987655 = 43.224159898

Reorder the terms:
43.20987655 + x = 43.224159898

Solving
43.20987655 + x = 43.224159898

Solving for variable 'x'.

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

Add '-43.20987655' to each side of the equation.
43.20987655 + -43.20987655 + x = 43.224159898 + -43.20987655

Combine like terms: 43.20987655 + -43.20987655 = 0.00000000
0.00000000 + x = 43.224159898 + -43.20987655
x = 43.224159898 + -43.20987655

Combine like terms: 43.224159898 + -43.20987655 = 0.014283348
x = 0.014283348

Simplifying
x = 0.014283348

Subproblem 2
x + 43.20987655 = -43.224159898

Simplifying
x + 43.20987655 = -43.224159898

Reorder the terms:
43.20987655 + x = -43.224159898

Solving
43.20987655 + x = -43.224159898

Solving for variable 'x'.

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

Add '-43.20987655' to each side of the equation.
43.20987655 + -43.20987655 + x = -43.224159898 + -43.20987655

Combine like terms: 43.20987655 + -43.20987655 = 0.00000000
0.00000000 + x = -43.224159898 + -43.20987655
x = -43.224159898 + -43.20987655

Combine like terms: -43.224159898 + -43.20987655 = -86.434036448
x = -86.434036448

Simplifying
x = -86.434036448

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.014283348, -86.434036448}