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Simplifying d2 + -8d + 4 = 0 Reorder the terms: 4 + -8d + d2 = 0 Solving 4 + -8d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8d + -4 + d2 = 0 + -4 Reorder the terms: 4 + -4 + -8d + d2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8d + d2 = 0 + -4 -8d + d2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8d + d2 = -4 The d term is -8d. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8d + 16 + d2 = -4 + 16 Reorder the terms: 16 + -8d + d2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8d + d2 = 12 Factor a perfect square on the left side: (d + -4)(d + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (d + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
d + -4 = 3.464101615 Simplifying d + -4 = 3.464101615 Reorder the terms: -4 + d = 3.464101615 Solving -4 + d = 3.464101615 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + d = 3.464101615 + 4 d = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 d = 7.464101615 Simplifying d = 7.464101615Subproblem 2
d + -4 = -3.464101615 Simplifying d + -4 = -3.464101615 Reorder the terms: -4 + d = -3.464101615 Solving -4 + d = -3.464101615 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + d = -3.464101615 + 4 d = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 d = 0.535898385 Simplifying d = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.464101615, 0.535898385}
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