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Simplifying 3(j + 7) = 7j2 Reorder the terms: 3(7 + j) = 7j2 (7 * 3 + j * 3) = 7j2 (21 + 3j) = 7j2 Solving 21 + 3j = 7j2 Solving for variable 'j'. Combine like terms: 7j2 + -7j2 = 0 21 + 3j + -7j2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3 + -0.4285714286j + j2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.4285714286j + 3 + j2 = 0 + 3 Reorder the terms: -3 + 3 + -0.4285714286j + j2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.4285714286j + j2 = 0 + 3 -0.4285714286j + j2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.4285714286j + j2 = 3 The j term is -0.4285714286j. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286j + 0.04591836735 + j2 = 3 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286j + j2 = 3 + 0.04591836735 Combine like terms: 3 + 0.04591836735 = 3.04591836735 0.04591836735 + -0.4285714286j + j2 = 3.04591836735 Factor a perfect square on the left side: (j + -0.2142857143)(j + -0.2142857143) = 3.04591836735 Calculate the square root of the right side: 1.74525596 Break this problem into two subproblems by setting (j + -0.2142857143) equal to 1.74525596 and -1.74525596.Subproblem 1
j + -0.2142857143 = 1.74525596 Simplifying j + -0.2142857143 = 1.74525596 Reorder the terms: -0.2142857143 + j = 1.74525596 Solving -0.2142857143 + j = 1.74525596 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + j = 1.74525596 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + j = 1.74525596 + 0.2142857143 j = 1.74525596 + 0.2142857143 Combine like terms: 1.74525596 + 0.2142857143 = 1.9595416743 j = 1.9595416743 Simplifying j = 1.9595416743Subproblem 2
j + -0.2142857143 = -1.74525596 Simplifying j + -0.2142857143 = -1.74525596 Reorder the terms: -0.2142857143 + j = -1.74525596 Solving -0.2142857143 + j = -1.74525596 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + j = -1.74525596 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + j = -1.74525596 + 0.2142857143 j = -1.74525596 + 0.2142857143 Combine like terms: -1.74525596 + 0.2142857143 = -1.5309702457 j = -1.5309702457 Simplifying j = -1.5309702457Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.9595416743, -1.5309702457}
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