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Simplifying d2 + -24d + 114 = 0 Reorder the terms: 114 + -24d + d2 = 0 Solving 114 + -24d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-114' to each side of the equation. 114 + -24d + -114 + d2 = 0 + -114 Reorder the terms: 114 + -114 + -24d + d2 = 0 + -114 Combine like terms: 114 + -114 = 0 0 + -24d + d2 = 0 + -114 -24d + d2 = 0 + -114 Combine like terms: 0 + -114 = -114 -24d + d2 = -114 The d term is -24d. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24d + 144 + d2 = -114 + 144 Reorder the terms: 144 + -24d + d2 = -114 + 144 Combine like terms: -114 + 144 = 30 144 + -24d + d2 = 30 Factor a perfect square on the left side: (d + -12)(d + -12) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (d + -12) equal to 5.477225575 and -5.477225575.Subproblem 1
d + -12 = 5.477225575 Simplifying d + -12 = 5.477225575 Reorder the terms: -12 + d = 5.477225575 Solving -12 + d = 5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + d = 5.477225575 + 12 Combine like terms: -12 + 12 = 0 0 + d = 5.477225575 + 12 d = 5.477225575 + 12 Combine like terms: 5.477225575 + 12 = 17.477225575 d = 17.477225575 Simplifying d = 17.477225575Subproblem 2
d + -12 = -5.477225575 Simplifying d + -12 = -5.477225575 Reorder the terms: -12 + d = -5.477225575 Solving -12 + d = -5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + d = -5.477225575 + 12 Combine like terms: -12 + 12 = 0 0 + d = -5.477225575 + 12 d = -5.477225575 + 12 Combine like terms: -5.477225575 + 12 = 6.522774425 d = 6.522774425 Simplifying d = 6.522774425Solution
The solution to the problem is based on the solutions from the subproblems. d = {17.477225575, 6.522774425}
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