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Simplifying d2 + -10d + 25 = 6 Reorder the terms: 25 + -10d + d2 = 6 Solving 25 + -10d + d2 = 6 Solving for variable 'd'. Reorder the terms: 25 + -6 + -10d + d2 = 6 + -6 Combine like terms: 25 + -6 = 19 19 + -10d + d2 = 6 + -6 Combine like terms: 6 + -6 = 0 19 + -10d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -10d + -19 + d2 = 0 + -19 Reorder the terms: 19 + -19 + -10d + d2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -10d + d2 = 0 + -19 -10d + d2 = 0 + -19 Combine like terms: 0 + -19 = -19 -10d + d2 = -19 The d term is -10d. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10d + 25 + d2 = -19 + 25 Reorder the terms: 25 + -10d + d2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + -10d + d2 = 6 Factor a perfect square on the left side: (d + -5)(d + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (d + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
d + -5 = 2.449489743 Simplifying d + -5 = 2.449489743 Reorder the terms: -5 + d = 2.449489743 Solving -5 + d = 2.449489743 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + d = 2.449489743 + 5 d = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 d = 7.449489743 Simplifying d = 7.449489743Subproblem 2
d + -5 = -2.449489743 Simplifying d + -5 = -2.449489743 Reorder the terms: -5 + d = -2.449489743 Solving -5 + d = -2.449489743 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + d = -2.449489743 + 5 d = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 d = 2.550510257 Simplifying d = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.449489743, 2.550510257}
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