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Simplifying d2 + 10d = 49 Reorder the terms: 10d + d2 = 49 Solving 10d + d2 = 49 Solving for variable 'd'. Reorder the terms: -49 + 10d + d2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 10d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 10d + 49 + d2 = 0 + 49 Reorder the terms: -49 + 49 + 10d + d2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 10d + d2 = 0 + 49 10d + d2 = 0 + 49 Combine like terms: 0 + 49 = 49 10d + d2 = 49 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 = 49 + 25 Reorder the terms: 25 + 10d + d2 = 49 + 25 Combine like terms: 49 + 25 = 74 25 + 10d + d2 = 74 Factor a perfect square on the left side: (d + 5)(d + 5) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (d + 5) equal to 8.602325267 and -8.602325267.Subproblem 1
d + 5 = 8.602325267 Simplifying d + 5 = 8.602325267 Reorder the terms: 5 + d = 8.602325267 Solving 5 + d = 8.602325267 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 = 8.602325267 + -5 Combine like terms: 5 + -5 = 0 0 + d = 8.602325267 + -5 d = 8.602325267 + -5 Combine like terms: 8.602325267 + -5 = 3.602325267 d = 3.602325267 Simplifying d = 3.602325267Subproblem 2
d + 5 = -8.602325267 Simplifying d + 5 = -8.602325267 Reorder the terms: 5 + d = -8.602325267 Solving 5 + d = -8.602325267 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 = -8.602325267 + -5 Combine like terms: 5 + -5 = 0 0 + d = -8.602325267 + -5 d = -8.602325267 + -5 Combine like terms: -8.602325267 + -5 = -13.602325267 d = -13.602325267 Simplifying d = -13.602325267Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.602325267, -13.602325267}
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