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Simplifying j2 + 28j + -11 = 0 Reorder the terms: -11 + 28j + j2 = 0 Solving -11 + 28j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 28j + 11 + j2 = 0 + 11 Reorder the terms: -11 + 11 + 28j + j2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 28j + j2 = 0 + 11 28j + j2 = 0 + 11 Combine like terms: 0 + 11 = 11 28j + j2 = 11 The j term is 28j. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28j + 196 + j2 = 11 + 196 Reorder the terms: 196 + 28j + j2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + 28j + j2 = 207 Factor a perfect square on the left side: (j + 14)(j + 14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (j + 14) equal to 14.38749457 and -14.38749457.Subproblem 1
j + 14 = 14.38749457 Simplifying j + 14 = 14.38749457 Reorder the terms: 14 + j = 14.38749457 Solving 14 + j = 14.38749457 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + j = 14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + j = 14.38749457 + -14 j = 14.38749457 + -14 Combine like terms: 14.38749457 + -14 = 0.38749457 j = 0.38749457 Simplifying j = 0.38749457Subproblem 2
j + 14 = -14.38749457 Simplifying j + 14 = -14.38749457 Reorder the terms: 14 + j = -14.38749457 Solving 14 + j = -14.38749457 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + j = -14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + j = -14.38749457 + -14 j = -14.38749457 + -14 Combine like terms: -14.38749457 + -14 = -28.38749457 j = -28.38749457 Simplifying j = -28.38749457Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.38749457, -28.38749457}
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