j^2+8j+8=0

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Solution for j^2+8j+8=0 equation:


Simplifying
j2 + 8j + 8 = 0

Reorder the terms:
8 + 8j + j2 = 0

Solving
8 + 8j + j2 = 0

Solving for variable 'j'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 8j + -8 + j2 = 0 + -8

Reorder the terms:
8 + -8 + 8j + j2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 8j + j2 = 0 + -8
8j + j2 = 0 + -8

Combine like terms: 0 + -8 = -8
8j + j2 = -8

The j term is 8j.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8j + 16 + j2 = -8 + 16

Reorder the terms:
16 + 8j + j2 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + 8j + j2 = 8

Factor a perfect square on the left side:
(j + 4)(j + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(j + 4) equal to 2.828427125 and -2.828427125.

Subproblem 1

j + 4 = 2.828427125 Simplifying j + 4 = 2.828427125 Reorder the terms: 4 + j = 2.828427125 Solving 4 + j = 2.828427125 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + j = 2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + j = 2.828427125 + -4 j = 2.828427125 + -4 Combine like terms: 2.828427125 + -4 = -1.171572875 j = -1.171572875 Simplifying j = -1.171572875

Subproblem 2

j + 4 = -2.828427125 Simplifying j + 4 = -2.828427125 Reorder the terms: 4 + j = -2.828427125 Solving 4 + j = -2.828427125 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + j = -2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + j = -2.828427125 + -4 j = -2.828427125 + -4 Combine like terms: -2.828427125 + -4 = -6.828427125 j = -6.828427125 Simplifying j = -6.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. j = {-1.171572875, -6.828427125}

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