x^2-12x-74=0

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Solution for x^2-12x-74=0 equation:


Simplifying
x2 + -12x + -74 = 0

Reorder the terms:
-74 + -12x + x2 = 0

Solving
-74 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + -12x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + -12x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + -12x + x2 = 0 + 74
-12x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
-12x + x2 = 74

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 = 74 + 36

Reorder the terms:
36 + -12x + x2 = 74 + 36

Combine like terms: 74 + 36 = 110
36 + -12x + x2 = 110

Factor a perfect square on the left side:
(x + -6)(x + -6) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(x + -6) equal to 10.488088482 and -10.488088482.

Subproblem 1

x + -6 = 10.488088482 Simplifying x + -6 = 10.488088482 Reorder the terms: -6 + x = 10.488088482 Solving -6 + x = 10.488088482 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 = 10.488088482 + 6 Combine like terms: -6 + 6 = 0 0 + x = 10.488088482 + 6 x = 10.488088482 + 6 Combine like terms: 10.488088482 + 6 = 16.488088482 x = 16.488088482 Simplifying x = 16.488088482

Subproblem 2

x + -6 = -10.488088482 Simplifying x + -6 = -10.488088482 Reorder the terms: -6 + x = -10.488088482 Solving -6 + x = -10.488088482 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 = -10.488088482 + 6 Combine like terms: -6 + 6 = 0 0 + x = -10.488088482 + 6 x = -10.488088482 + 6 Combine like terms: -10.488088482 + 6 = -4.488088482 x = -4.488088482 Simplifying x = -4.488088482

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.488088482, -4.488088482}

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