36=x*x+(x-3)

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Solution for 36=x*x+(x-3) equation:


Simplifying
36 = x * x + (x + -3)

Multiply x * x
36 = x2 + (x + -3)

Reorder the terms:
36 = x2 + (-3 + x)

Remove parenthesis around (-3 + x)
36 = x2 + -3 + x

Reorder the terms:
36 = -3 + x + x2

Solving
36 = -3 + x + x2

Solving for variable 'x'.

Combine like terms: 36 + 3 = 39
39 + -1x + -1x2 = -3 + x + x2 + 3 + -1x + -1x2

Reorder the terms:
39 + -1x + -1x2 = -3 + 3 + x + -1x + x2 + -1x2

Combine like terms: -3 + 3 = 0
39 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
39 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
39 + -1x + -1x2 = 0 + x2 + -1x2
39 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
39 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-39 + x + x2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + x + x2 = 0 + 39
x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
x + x2 = 39

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 39 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 39 + 0.25

Combine like terms: 39 + 0.25 = 39.25
1.25 + x2 = 39.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.264982043 and -6.264982043.

Subproblem 1

x + 0.5 = 6.264982043 Simplifying x + 0.5 = 6.264982043 Reorder the terms: 0.5 + x = 6.264982043 Solving 0.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.264982043 + -0.5 x = 6.264982043 + -0.5 Combine like terms: 6.264982043 + -0.5 = 5.764982043 x = 5.764982043 Simplifying x = 5.764982043

Subproblem 2

x + 0.5 = -6.264982043 Simplifying x + 0.5 = -6.264982043 Reorder the terms: 0.5 + x = -6.264982043 Solving 0.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.264982043 + -0.5 x = -6.264982043 + -0.5 Combine like terms: -6.264982043 + -0.5 = -6.764982043 x = -6.764982043 Simplifying x = -6.764982043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.764982043, -6.764982043}

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