j^2-8j=-11

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Solution for j^2-8j=-11 equation:


Simplifying
j2 + -8j = -11

Reorder the terms:
-8j + j2 = -11

Solving
-8j + j2 = -11

Solving for variable 'j'.

Reorder the terms:
11 + -8j + j2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + -8j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -8j + -11 + j2 = 0 + -11

Reorder the terms:
11 + -11 + -8j + j2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -8j + j2 = 0 + -11
-8j + j2 = 0 + -11

Combine like terms: 0 + -11 = -11
-8j + j2 = -11

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 = -11 + 16

Reorder the terms:
16 + -8j + j2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + -8j + j2 = 5

Factor a perfect square on the left side:
(j + -4)(j + -4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(j + -4) equal to 2.236067978 and -2.236067978.

Subproblem 1

j + -4 = 2.236067978 Simplifying j + -4 = 2.236067978 Reorder the terms: -4 + j = 2.236067978 Solving -4 + j = 2.236067978 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 = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + j = 2.236067978 + 4 j = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 j = 6.236067978 Simplifying j = 6.236067978

Subproblem 2

j + -4 = -2.236067978 Simplifying j + -4 = -2.236067978 Reorder the terms: -4 + j = -2.236067978 Solving -4 + j = -2.236067978 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 = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + j = -2.236067978 + 4 j = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 j = 1.763932022 Simplifying j = 1.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. j = {6.236067978, 1.763932022}

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