j^2-12j-49=0

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Solution for j^2-12j-49=0 equation:


Simplifying
j2 + -12j + -49 = 0

Reorder the terms:
-49 + -12j + j2 = 0

Solving
-49 + -12j + j2 = 0

Solving for variable 'j'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -12j + 49 + j2 = 0 + 49

Reorder the terms:
-49 + 49 + -12j + j2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -12j + j2 = 0 + 49
-12j + j2 = 0 + 49

Combine like terms: 0 + 49 = 49
-12j + j2 = 49

The j term is -12j.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12j + 36 + j2 = 49 + 36

Reorder the terms:
36 + -12j + j2 = 49 + 36

Combine like terms: 49 + 36 = 85
36 + -12j + j2 = 85

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

Calculate the square root of the right side: 9.219544457

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

Subproblem 1

j + -6 = 9.219544457 Simplifying j + -6 = 9.219544457 Reorder the terms: -6 + j = 9.219544457 Solving -6 + j = 9.219544457 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = 9.219544457 + 6 Combine like terms: -6 + 6 = 0 0 + j = 9.219544457 + 6 j = 9.219544457 + 6 Combine like terms: 9.219544457 + 6 = 15.219544457 j = 15.219544457 Simplifying j = 15.219544457

Subproblem 2

j + -6 = -9.219544457 Simplifying j + -6 = -9.219544457 Reorder the terms: -6 + j = -9.219544457 Solving -6 + j = -9.219544457 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = -9.219544457 + 6 Combine like terms: -6 + 6 = 0 0 + j = -9.219544457 + 6 j = -9.219544457 + 6 Combine like terms: -9.219544457 + 6 = -3.219544457 j = -3.219544457 Simplifying j = -3.219544457

Solution

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

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