x^2-12x-61=0

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Solution for x^2-12x-61=0 equation:


Simplifying
x2 + -12x + -61 = 0

Reorder the terms:
-61 + -12x + x2 = 0

Solving
-61 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + -12x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + -12x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -12x + x2 = 0 + 61
-12x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
-12x + x2 = 61

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 = 61 + 36

Reorder the terms:
36 + -12x + x2 = 61 + 36

Combine like terms: 61 + 36 = 97
36 + -12x + x2 = 97

Factor a perfect square on the left side:
(x + -6)(x + -6) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -6) equal to 9.848857802 and -9.848857802.

Subproblem 1

x + -6 = 9.848857802 Simplifying x + -6 = 9.848857802 Reorder the terms: -6 + x = 9.848857802 Solving -6 + x = 9.848857802 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 = 9.848857802 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.848857802 + 6 x = 9.848857802 + 6 Combine like terms: 9.848857802 + 6 = 15.848857802 x = 15.848857802 Simplifying x = 15.848857802

Subproblem 2

x + -6 = -9.848857802 Simplifying x + -6 = -9.848857802 Reorder the terms: -6 + x = -9.848857802 Solving -6 + x = -9.848857802 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 = -9.848857802 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.848857802 + 6 x = -9.848857802 + 6 Combine like terms: -9.848857802 + 6 = -3.848857802 x = -3.848857802 Simplifying x = -3.848857802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.848857802, -3.848857802}

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