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Simplifying 2j2 + 4j + -22 = 0 Reorder the terms: -22 + 4j + 2j2 = 0 Solving -22 + 4j + 2j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 2j + j2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 2j + j2)' equal to zero and attempt to solve: Simplifying -11 + 2j + j2 = 0 Solving -11 + 2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 2j + 11 + j2 = 0 + 11 Reorder the terms: -11 + 11 + 2j + j2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2j + j2 = 0 + 11 2j + j2 = 0 + 11 Combine like terms: 0 + 11 = 11 2j + j2 = 11 The j term is 2j. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2j + 1 + j2 = 11 + 1 Reorder the terms: 1 + 2j + j2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + 2j + j2 = 12 Factor a perfect square on the left side: (j + 1)(j + 1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (j + 1) equal to 3.464101615 and -3.464101615.Subproblem 1
j + 1 = 3.464101615 Simplifying j + 1 = 3.464101615 Reorder the terms: 1 + j = 3.464101615 Solving 1 + j = 3.464101615 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + j = 3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + j = 3.464101615 + -1 j = 3.464101615 + -1 Combine like terms: 3.464101615 + -1 = 2.464101615 j = 2.464101615 Simplifying j = 2.464101615Subproblem 2
j + 1 = -3.464101615 Simplifying j + 1 = -3.464101615 Reorder the terms: 1 + j = -3.464101615 Solving 1 + j = -3.464101615 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + j = -3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + j = -3.464101615 + -1 j = -3.464101615 + -1 Combine like terms: -3.464101615 + -1 = -4.464101615 j = -4.464101615 Simplifying j = -4.464101615Solution
The solution to the problem is based on the solutions from the subproblems. j = {2.464101615, -4.464101615}Solution
j = {2.464101615, -4.464101615}
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