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Simplifying d2 + -12d + 28 = 0 Reorder the terms: 28 + -12d + d2 = 0 Solving 28 + -12d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -12d + -28 + d2 = 0 + -28 Reorder the terms: 28 + -28 + -12d + d2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -12d + d2 = 0 + -28 -12d + d2 = 0 + -28 Combine like terms: 0 + -28 = -28 -12d + d2 = -28 The d term is -12d. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12d + 36 + d2 = -28 + 36 Reorder the terms: 36 + -12d + d2 = -28 + 36 Combine like terms: -28 + 36 = 8 36 + -12d + d2 = 8 Factor a perfect square on the left side: (d + -6)(d + -6) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (d + -6) equal to 2.828427125 and -2.828427125.Subproblem 1
d + -6 = 2.828427125 Simplifying d + -6 = 2.828427125 Reorder the terms: -6 + d = 2.828427125 Solving -6 + d = 2.828427125 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = 2.828427125 + 6 Combine like terms: -6 + 6 = 0 0 + d = 2.828427125 + 6 d = 2.828427125 + 6 Combine like terms: 2.828427125 + 6 = 8.828427125 d = 8.828427125 Simplifying d = 8.828427125Subproblem 2
d + -6 = -2.828427125 Simplifying d + -6 = -2.828427125 Reorder the terms: -6 + d = -2.828427125 Solving -6 + d = -2.828427125 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = -2.828427125 + 6 Combine like terms: -6 + 6 = 0 0 + d = -2.828427125 + 6 d = -2.828427125 + 6 Combine like terms: -2.828427125 + 6 = 3.171572875 d = 3.171572875 Simplifying d = 3.171572875Solution
The solution to the problem is based on the solutions from the subproblems. d = {8.828427125, 3.171572875}
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