x^2+6x+36=100

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Solution for x^2+6x+36=100 equation:


Simplifying
x2 + 6x + 36 = 100

Reorder the terms:
36 + 6x + x2 = 100

Solving
36 + 6x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
36 + -100 + 6x + x2 = 100 + -100

Combine like terms: 36 + -100 = -64
-64 + 6x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-64 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 6x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 6x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 6x + x2 = 0 + 64
6x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
6x + x2 = 64

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 64 + 9

Reorder the terms:
9 + 6x + x2 = 64 + 9

Combine like terms: 64 + 9 = 73
9 + 6x + x2 = 73

Factor a perfect square on the left side:
(x + 3)(x + 3) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 3) equal to 8.544003745 and -8.544003745.

Subproblem 1

x + 3 = 8.544003745 Simplifying x + 3 = 8.544003745 Reorder the terms: 3 + x = 8.544003745 Solving 3 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.544003745 + -3 x = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 x = 5.544003745 Simplifying x = 5.544003745

Subproblem 2

x + 3 = -8.544003745 Simplifying x + 3 = -8.544003745 Reorder the terms: 3 + x = -8.544003745 Solving 3 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.544003745 + -3 x = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 x = -11.544003745 Simplifying x = -11.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.544003745, -11.544003745}

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