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Simplifying d2 + 56 = -19d Reorder the terms: 56 + d2 = -19d Solving 56 + d2 = -19d Solving for variable 'd'. Reorder the terms: 56 + 19d + d2 = -19d + 19d Combine like terms: -19d + 19d = 0 56 + 19d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 19d + -56 + d2 = 0 + -56 Reorder the terms: 56 + -56 + 19d + d2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 19d + d2 = 0 + -56 19d + d2 = 0 + -56 Combine like terms: 0 + -56 = -56 19d + d2 = -56 The d term is 19d. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19d + 90.25 + d2 = -56 + 90.25 Reorder the terms: 90.25 + 19d + d2 = -56 + 90.25 Combine like terms: -56 + 90.25 = 34.25 90.25 + 19d + d2 = 34.25 Factor a perfect square on the left side: (d + 9.5)(d + 9.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (d + 9.5) equal to 5.852349955 and -5.852349955.Subproblem 1
d + 9.5 = 5.852349955 Simplifying d + 9.5 = 5.852349955 Reorder the terms: 9.5 + d = 5.852349955 Solving 9.5 + d = 5.852349955 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + d = 5.852349955 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + d = 5.852349955 + -9.5 d = 5.852349955 + -9.5 Combine like terms: 5.852349955 + -9.5 = -3.647650045 d = -3.647650045 Simplifying d = -3.647650045Subproblem 2
d + 9.5 = -5.852349955 Simplifying d + 9.5 = -5.852349955 Reorder the terms: 9.5 + d = -5.852349955 Solving 9.5 + d = -5.852349955 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + d = -5.852349955 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + d = -5.852349955 + -9.5 d = -5.852349955 + -9.5 Combine like terms: -5.852349955 + -9.5 = -15.352349955 d = -15.352349955 Simplifying d = -15.352349955Solution
The solution to the problem is based on the solutions from the subproblems. d = {-3.647650045, -15.352349955}
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