x^2-(12x)=10

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Solution for x^2-(12x)=10 equation:


Simplifying
x2 + -1(12x) = 10

Remove parenthesis around (12x)
x2 + -1 * 12x = 10

Multiply -1 * 12
x2 + -12x = 10

Reorder the terms:
-12x + x2 = 10

Solving
-12x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -12x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -12x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -12x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -12x + x2 = 0 + 10
-12x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-12x + x2 = 10

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 = 10 + 36

Reorder the terms:
36 + -12x + x2 = 10 + 36

Combine like terms: 10 + 36 = 46
36 + -12x + x2 = 46

Factor a perfect square on the left side:
(x + -6)(x + -6) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + -6) equal to 6.782329983 and -6.782329983.

Subproblem 1

x + -6 = 6.782329983 Simplifying x + -6 = 6.782329983 Reorder the terms: -6 + x = 6.782329983 Solving -6 + x = 6.782329983 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 = 6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.782329983 + 6 x = 6.782329983 + 6 Combine like terms: 6.782329983 + 6 = 12.782329983 x = 12.782329983 Simplifying x = 12.782329983

Subproblem 2

x + -6 = -6.782329983 Simplifying x + -6 = -6.782329983 Reorder the terms: -6 + x = -6.782329983 Solving -6 + x = -6.782329983 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 = -6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.782329983 + 6 x = -6.782329983 + 6 Combine like terms: -6.782329983 + 6 = -0.782329983 x = -0.782329983 Simplifying x = -0.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.782329983, -0.782329983}

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