x^2-12x=35

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Solution for x^2-12x=35 equation:


Simplifying
x2 + -12x = 35

Reorder the terms:
-12x + x2 = 35

Solving
-12x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -12x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -12x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -12x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -12x + x2 = 0 + 35
-12x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-12x + x2 = 35

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 = 35 + 36

Reorder the terms:
36 + -12x + x2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + -12x + x2 = 71

Factor a perfect square on the left side:
(x + -6)(x + -6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + -6) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + -6 = 8.426149773 Simplifying x + -6 = 8.426149773 Reorder the terms: -6 + x = 8.426149773 Solving -6 + x = 8.426149773 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 = 8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.426149773 + 6 x = 8.426149773 + 6 Combine like terms: 8.426149773 + 6 = 14.426149773 x = 14.426149773 Simplifying x = 14.426149773

Subproblem 2

x + -6 = -8.426149773 Simplifying x + -6 = -8.426149773 Reorder the terms: -6 + x = -8.426149773 Solving -6 + x = -8.426149773 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 = -8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.426149773 + 6 x = -8.426149773 + 6 Combine like terms: -8.426149773 + 6 = -2.426149773 x = -2.426149773 Simplifying x = -2.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.426149773, -2.426149773}

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