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Simplifying d2 + -8d + -12 = 2 Reorder the terms: -12 + -8d + d2 = 2 Solving -12 + -8d + d2 = 2 Solving for variable 'd'. Reorder the terms: -12 + -2 + -8d + d2 = 2 + -2 Combine like terms: -12 + -2 = -14 -14 + -8d + d2 = 2 + -2 Combine like terms: 2 + -2 = 0 -14 + -8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -8d + 14 + d2 = 0 + 14 Reorder the terms: -14 + 14 + -8d + d2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -8d + d2 = 0 + 14 -8d + d2 = 0 + 14 Combine like terms: 0 + 14 = 14 -8d + d2 = 14 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 = 14 + 16 Reorder the terms: 16 + -8d + d2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + -8d + d2 = 30 Factor a perfect square on the left side: (d + -4)(d + -4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (d + -4) equal to 5.477225575 and -5.477225575.Subproblem 1
d + -4 = 5.477225575 Simplifying d + -4 = 5.477225575 Reorder the terms: -4 + d = 5.477225575 Solving -4 + d = 5.477225575 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 = 5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + d = 5.477225575 + 4 d = 5.477225575 + 4 Combine like terms: 5.477225575 + 4 = 9.477225575 d = 9.477225575 Simplifying d = 9.477225575Subproblem 2
d + -4 = -5.477225575 Simplifying d + -4 = -5.477225575 Reorder the terms: -4 + d = -5.477225575 Solving -4 + d = -5.477225575 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 = -5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + d = -5.477225575 + 4 d = -5.477225575 + 4 Combine like terms: -5.477225575 + 4 = -1.477225575 d = -1.477225575 Simplifying d = -1.477225575Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.477225575, -1.477225575}
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