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Simplifying 5j2 + 4j = 100 Reorder the terms: 4j + 5j2 = 100 Solving 4j + 5j2 = 100 Solving for variable 'j'. Reorder the terms: -100 + 4j + 5j2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 4j + 5j2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + 0.8j + j2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 0.8j + 20 + j2 = 0 + 20 Reorder the terms: -20 + 20 + 0.8j + j2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 0.8j + j2 = 0 + 20 0.8j + j2 = 0 + 20 Combine like terms: 0 + 20 = 20 0.8j + j2 = 20 The j term is 0.8j. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8j + 0.16 + j2 = 20 + 0.16 Reorder the terms: 0.16 + 0.8j + j2 = 20 + 0.16 Combine like terms: 20 + 0.16 = 20.16 0.16 + 0.8j + j2 = 20.16 Factor a perfect square on the left side: (j + 0.4)(j + 0.4) = 20.16 Calculate the square root of the right side: 4.489988864 Break this problem into two subproblems by setting (j + 0.4) equal to 4.489988864 and -4.489988864.Subproblem 1
j + 0.4 = 4.489988864 Simplifying j + 0.4 = 4.489988864 Reorder the terms: 0.4 + j = 4.489988864 Solving 0.4 + j = 4.489988864 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + j = 4.489988864 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + j = 4.489988864 + -0.4 j = 4.489988864 + -0.4 Combine like terms: 4.489988864 + -0.4 = 4.089988864 j = 4.089988864 Simplifying j = 4.089988864Subproblem 2
j + 0.4 = -4.489988864 Simplifying j + 0.4 = -4.489988864 Reorder the terms: 0.4 + j = -4.489988864 Solving 0.4 + j = -4.489988864 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + j = -4.489988864 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + j = -4.489988864 + -0.4 j = -4.489988864 + -0.4 Combine like terms: -4.489988864 + -0.4 = -4.889988864 j = -4.889988864 Simplifying j = -4.889988864Solution
The solution to the problem is based on the solutions from the subproblems. j = {4.089988864, -4.889988864}
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