12x+x^2=68

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Solution for 12x+x^2=68 equation:


Simplifying
12x + x2 = 68

Solving
12x + x2 = 68

Solving for variable 'x'.

Reorder the terms:
-68 + 12x + x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-68 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 12x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + 12x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 12x + x2 = 0 + 68
12x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
12x + x2 = 68

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 68 + 36

Reorder the terms:
36 + 12x + x2 = 68 + 36

Combine like terms: 68 + 36 = 104
36 + 12x + x2 = 104

Factor a perfect square on the left side:
(x + 6)(x + 6) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(x + 6) equal to 10.198039027 and -10.198039027.

Subproblem 1

x + 6 = 10.198039027 Simplifying x + 6 = 10.198039027 Reorder the terms: 6 + x = 10.198039027 Solving 6 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 10.198039027 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.198039027 + -6 x = 10.198039027 + -6 Combine like terms: 10.198039027 + -6 = 4.198039027 x = 4.198039027 Simplifying x = 4.198039027

Subproblem 2

x + 6 = -10.198039027 Simplifying x + 6 = -10.198039027 Reorder the terms: 6 + x = -10.198039027 Solving 6 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -10.198039027 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.198039027 + -6 x = -10.198039027 + -6 Combine like terms: -10.198039027 + -6 = -16.198039027 x = -16.198039027 Simplifying x = -16.198039027

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.198039027, -16.198039027}

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