7x^2-36x-405=

Solution for 7x^2-36x-405= equation:

Simplifying
7x2 + -36x + -405 = 0

Reorder the terms:
-405 + -36x + 7x2 = 0

Solving
-405 + -36x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-57.85714286 + -5.142857143x + x2 = 0

Move the constant term to the right:

Add '57.85714286' to each side of the equation.
-57.85714286 + -5.142857143x + 57.85714286 + x2 = 0 + 57.85714286

Reorder the terms:
-57.85714286 + 57.85714286 + -5.142857143x + x2 = 0 + 57.85714286

Combine like terms: -57.85714286 + 57.85714286 = 0.00000000
0.00000000 + -5.142857143x + x2 = 0 + 57.85714286
-5.142857143x + x2 = 0 + 57.85714286

Combine like terms: 0 + 57.85714286 = 57.85714286
-5.142857143x + x2 = 57.85714286

The x term is -5.142857143x.  Take half its coefficient (-2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
-5.142857143x + 6.612244901 + x2 = 57.85714286 + 6.612244901

Reorder the terms:
6.612244901 + -5.142857143x + x2 = 57.85714286 + 6.612244901

Combine like terms: 57.85714286 + 6.612244901 = 64.469387761
6.612244901 + -5.142857143x + x2 = 64.469387761

Factor a perfect square on the left side:
(x + -2.571428572)(x + -2.571428572) = 64.469387761

Calculate the square root of the right side: 8.029283141

Break this problem into two subproblems by setting 
(x + -2.571428572) equal to 8.029283141 and -8.029283141.

Subproblem 1
x + -2.571428572 = 8.029283141

Simplifying
x + -2.571428572 = 8.029283141

Reorder the terms:
-2.571428572 + x = 8.029283141

Solving
-2.571428572 + x = 8.029283141

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = 8.029283141 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = 8.029283141 + 2.571428572
x = 8.029283141 + 2.571428572

Combine like terms: 8.029283141 + 2.571428572 = 10.600711713
x = 10.600711713

Simplifying
x = 10.600711713

Subproblem 2
x + -2.571428572 = -8.029283141

Simplifying
x + -2.571428572 = -8.029283141

Reorder the terms:
-2.571428572 + x = -8.029283141

Solving
-2.571428572 + x = -8.029283141

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = -8.029283141 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = -8.029283141 + 2.571428572
x = -8.029283141 + 2.571428572

Combine like terms: -8.029283141 + 2.571428572 = -5.457854569
x = -5.457854569

Simplifying
x = -5.457854569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.600711713, -5.457854569}