x^2=128+12x

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Solution for x^2=128+12x equation:


Simplifying
x2 = 128 + 12x

Solving
x2 = 128 + 12x

Solving for variable 'x'.

Reorder the terms:
-128 + -12x + x2 = 128 + 12x + -128 + -12x

Reorder the terms:
-128 + -12x + x2 = 128 + -128 + 12x + -12x

Combine like terms: 128 + -128 = 0
-128 + -12x + x2 = 0 + 12x + -12x
-128 + -12x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-128 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + -12x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + -12x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + -12x + x2 = 0 + 128
-12x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
-12x + x2 = 128

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 = 128 + 36

Reorder the terms:
36 + -12x + x2 = 128 + 36

Combine like terms: 128 + 36 = 164
36 + -12x + x2 = 164

Factor a perfect square on the left side:
(x + -6)(x + -6) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(x + -6) equal to 12.806248475 and -12.806248475.

Subproblem 1

x + -6 = 12.806248475 Simplifying x + -6 = 12.806248475 Reorder the terms: -6 + x = 12.806248475 Solving -6 + x = 12.806248475 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 = 12.806248475 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.806248475 + 6 x = 12.806248475 + 6 Combine like terms: 12.806248475 + 6 = 18.806248475 x = 18.806248475 Simplifying x = 18.806248475

Subproblem 2

x + -6 = -12.806248475 Simplifying x + -6 = -12.806248475 Reorder the terms: -6 + x = -12.806248475 Solving -6 + x = -12.806248475 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 = -12.806248475 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.806248475 + 6 x = -12.806248475 + 6 Combine like terms: -12.806248475 + 6 = -6.806248475 x = -6.806248475 Simplifying x = -6.806248475

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.806248475, -6.806248475}

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