36.7=x^2-7x

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Solution for 36.7=x^2-7x equation: 


Simplifying
36.7 = x2 + -7x

Reorder the terms:
36.7 = -7x + x2

Solving
36.7 = -7x + x2

Solving for variable 'x'.

Reorder the terms:
36.7 + 7x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
36.7 + 7x + -1x2 = 0 + x2 + -1x2
36.7 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36.7 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-36.7 + -7x + x2 = 0

Move the constant term to the right:

Add '36.7' to each side of the equation.
-36.7 + -7x + 36.7 + x2 = 0 + 36.7

Reorder the terms:
-36.7 + 36.7 + -7x + x2 = 0 + 36.7

Combine like terms: -36.7 + 36.7 = 0.0
0.0 + -7x + x2 = 0 + 36.7
-7x + x2 = 0 + 36.7

Combine like terms: 0 + 36.7 = 36.7
-7x + x2 = 36.7

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 36.7 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 36.7 + 12.25

Combine like terms: 36.7 + 12.25 = 48.95
12.25 + -7x + x2 = 48.95

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 48.95

Calculate the square root of the right side: 6.99642766

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.99642766 and -6.99642766.


Subproblem 1
x + -3.5 = 6.99642766

Simplifying
x + -3.5 = 6.99642766

Reorder the terms:
-3.5 + x = 6.99642766

Solving
-3.5 + x = 6.99642766

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 6.99642766 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.99642766 + 3.5
x = 6.99642766 + 3.5

Combine like terms: 6.99642766 + 3.5 = 10.49642766
x = 10.49642766

Simplifying
x = 10.49642766


Subproblem 2
x + -3.5 = -6.99642766

Simplifying
x + -3.5 = -6.99642766

Reorder the terms:
-3.5 + x = -6.99642766

Solving
-3.5 + x = -6.99642766

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -6.99642766 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.99642766 + 3.5
x = -6.99642766 + 3.5

Combine like terms: -6.99642766 + 3.5 = -3.49642766
x = -3.49642766

Simplifying
x = -3.49642766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.49642766, -3.49642766}

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