144=6x+x^2

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Solution for 144=6x+x^2 equation:


Simplifying
144 = 6x + x2

Solving
144 = 6x + x2

Solving for variable 'x'.

Reorder the terms:
144 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
144 + -6x + -1x2 = 0 + x2 + -1x2
144 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
144 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-144 + 6x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 6x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 6x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 6x + x2 = 0 + 144
6x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
6x + x2 = 144

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 = 144 + 9

Reorder the terms:
9 + 6x + x2 = 144 + 9

Combine like terms: 144 + 9 = 153
9 + 6x + x2 = 153

Factor a perfect square on the left side:
(x + 3)(x + 3) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + 3) equal to 12.369316877 and -12.369316877.

Subproblem 1

x + 3 = 12.369316877 Simplifying x + 3 = 12.369316877 Reorder the terms: 3 + x = 12.369316877 Solving 3 + x = 12.369316877 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 = 12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.369316877 + -3 x = 12.369316877 + -3 Combine like terms: 12.369316877 + -3 = 9.369316877 x = 9.369316877 Simplifying x = 9.369316877

Subproblem 2

x + 3 = -12.369316877 Simplifying x + 3 = -12.369316877 Reorder the terms: 3 + x = -12.369316877 Solving 3 + x = -12.369316877 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 = -12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.369316877 + -3 x = -12.369316877 + -3 Combine like terms: -12.369316877 + -3 = -15.369316877 x = -15.369316877 Simplifying x = -15.369316877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.369316877, -15.369316877}

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