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Simplifying d2 + -24d + -47 = 0 Reorder the terms: -47 + -24d + d2 = 0 Solving -47 + -24d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -24d + 47 + d2 = 0 + 47 Reorder the terms: -47 + 47 + -24d + d2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -24d + d2 = 0 + 47 -24d + d2 = 0 + 47 Combine like terms: 0 + 47 = 47 -24d + d2 = 47 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 = 47 + 144 Reorder the terms: 144 + -24d + d2 = 47 + 144 Combine like terms: 47 + 144 = 191 144 + -24d + d2 = 191 Factor a perfect square on the left side: (d + -12)(d + -12) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (d + -12) equal to 13.820274961 and -13.820274961.Subproblem 1
d + -12 = 13.820274961 Simplifying d + -12 = 13.820274961 Reorder the terms: -12 + d = 13.820274961 Solving -12 + d = 13.820274961 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 = 13.820274961 + 12 Combine like terms: -12 + 12 = 0 0 + d = 13.820274961 + 12 d = 13.820274961 + 12 Combine like terms: 13.820274961 + 12 = 25.820274961 d = 25.820274961 Simplifying d = 25.820274961Subproblem 2
d + -12 = -13.820274961 Simplifying d + -12 = -13.820274961 Reorder the terms: -12 + d = -13.820274961 Solving -12 + d = -13.820274961 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 = -13.820274961 + 12 Combine like terms: -12 + 12 = 0 0 + d = -13.820274961 + 12 d = -13.820274961 + 12 Combine like terms: -13.820274961 + 12 = -1.820274961 d = -1.820274961 Simplifying d = -1.820274961Solution
The solution to the problem is based on the solutions from the subproblems. d = {25.820274961, -1.820274961}
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