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Simplifying 3d2 + 20d = 12 Reorder the terms: 20d + 3d2 = 12 Solving 20d + 3d2 = 12 Solving for variable 'd'. Reorder the terms: -12 + 20d + 3d2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 20d + 3d2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 6.666666667d + d2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6.666666667d + 4 + d2 = 0 + 4 Reorder the terms: -4 + 4 + 6.666666667d + d2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6.666666667d + d2 = 0 + 4 6.666666667d + d2 = 0 + 4 Combine like terms: 0 + 4 = 4 6.666666667d + d2 = 4 The d term is 6.666666667d. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667d + 11.11111112 + d2 = 4 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667d + d2 = 4 + 11.11111112 Combine like terms: 4 + 11.11111112 = 15.11111112 11.11111112 + 6.666666667d + d2 = 15.11111112 Factor a perfect square on the left side: (d + 3.333333334)(d + 3.333333334) = 15.11111112 Calculate the square root of the right side: 3.887301264 Break this problem into two subproblems by setting (d + 3.333333334) equal to 3.887301264 and -3.887301264.Subproblem 1
d + 3.333333334 = 3.887301264 Simplifying d + 3.333333334 = 3.887301264 Reorder the terms: 3.333333334 + d = 3.887301264 Solving 3.333333334 + d = 3.887301264 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + d = 3.887301264 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + d = 3.887301264 + -3.333333334 d = 3.887301264 + -3.333333334 Combine like terms: 3.887301264 + -3.333333334 = 0.55396793 d = 0.55396793 Simplifying d = 0.55396793Subproblem 2
d + 3.333333334 = -3.887301264 Simplifying d + 3.333333334 = -3.887301264 Reorder the terms: 3.333333334 + d = -3.887301264 Solving 3.333333334 + d = -3.887301264 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + d = -3.887301264 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + d = -3.887301264 + -3.333333334 d = -3.887301264 + -3.333333334 Combine like terms: -3.887301264 + -3.333333334 = -7.220634598 d = -7.220634598 Simplifying d = -7.220634598Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.55396793, -7.220634598}
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