x^2+33x+7=6x+18

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Solution for x^2+33x+7=6x+18 equation:


Simplifying
x2 + 33x + 7 = 6x + 18

Reorder the terms:
7 + 33x + x2 = 6x + 18

Reorder the terms:
7 + 33x + x2 = 18 + 6x

Solving
7 + 33x + x2 = 18 + 6x

Solving for variable 'x'.

Reorder the terms:
7 + -18 + 33x + -6x + x2 = 18 + 6x + -18 + -6x

Combine like terms: 7 + -18 = -11
-11 + 33x + -6x + x2 = 18 + 6x + -18 + -6x

Combine like terms: 33x + -6x = 27x
-11 + 27x + x2 = 18 + 6x + -18 + -6x

Reorder the terms:
-11 + 27x + x2 = 18 + -18 + 6x + -6x

Combine like terms: 18 + -18 = 0
-11 + 27x + x2 = 0 + 6x + -6x
-11 + 27x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-11 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 27x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 27x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 27x + x2 = 0 + 11
27x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
27x + x2 = 11

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = 11 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 11 + 182.25

Combine like terms: 11 + 182.25 = 193.25
182.25 + 27x + x2 = 193.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 193.25

Calculate the square root of the right side: 13.901438774

Break this problem into two subproblems by setting 
(x + 13.5) equal to 13.901438774 and -13.901438774.

Subproblem 1

x + 13.5 = 13.901438774 Simplifying x + 13.5 = 13.901438774 Reorder the terms: 13.5 + x = 13.901438774 Solving 13.5 + x = 13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.901438774 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.901438774 + -13.5 x = 13.901438774 + -13.5 Combine like terms: 13.901438774 + -13.5 = 0.401438774 x = 0.401438774 Simplifying x = 0.401438774

Subproblem 2

x + 13.5 = -13.901438774 Simplifying x + 13.5 = -13.901438774 Reorder the terms: 13.5 + x = -13.901438774 Solving 13.5 + x = -13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.901438774 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.901438774 + -13.5 x = -13.901438774 + -13.5 Combine like terms: -13.901438774 + -13.5 = -27.401438774 x = -27.401438774 Simplifying x = -27.401438774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.401438774, -27.401438774}

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