0=x^2+12x-49

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Solution for 0=x^2+12x-49 equation:


Simplifying
0 = x2 + 12x + -49

Reorder the terms:
0 = -49 + 12x + x2

Solving
0 = -49 + 12x + x2

Solving for variable 'x'.

Combine like terms: 0 + 49 = 49
49 + -12x + -1x2 = -49 + 12x + x2 + 49 + -12x + -1x2

Reorder the terms:
49 + -12x + -1x2 = -49 + 49 + 12x + -12x + x2 + -1x2

Combine like terms: -49 + 49 = 0
49 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
49 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
49 + -12x + -1x2 = 0 + x2 + -1x2
49 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
49 + -12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-49 + 12x + x2 = 0

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 12x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + 12x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 12x + x2 = 0 + 49
12x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
12x + x2 = 49

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 = 49 + 36

Reorder the terms:
36 + 12x + x2 = 49 + 36

Combine like terms: 49 + 36 = 85
36 + 12x + x2 = 85

Factor a perfect square on the left side:
(x + 6)(x + 6) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 6) equal to 9.219544457 and -9.219544457.

Subproblem 1

x + 6 = 9.219544457 Simplifying x + 6 = 9.219544457 Reorder the terms: 6 + x = 9.219544457 Solving 6 + x = 9.219544457 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 = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.219544457 + -6 x = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 x = 3.219544457 Simplifying x = 3.219544457

Subproblem 2

x + 6 = -9.219544457 Simplifying x + 6 = -9.219544457 Reorder the terms: 6 + x = -9.219544457 Solving 6 + x = -9.219544457 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 = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.219544457 + -6 x = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 x = -15.219544457 Simplifying x = -15.219544457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.219544457, -15.219544457}

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