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Simplifying d2 + -30d = 23 Reorder the terms: -30d + d2 = 23 Solving -30d + d2 = 23 Solving for variable 'd'. Reorder the terms: -23 + -30d + d2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -30d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -30d + 23 + d2 = 0 + 23 Reorder the terms: -23 + 23 + -30d + d2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -30d + d2 = 0 + 23 -30d + d2 = 0 + 23 Combine like terms: 0 + 23 = 23 -30d + d2 = 23 The d term is -30d. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30d + 225 + d2 = 23 + 225 Reorder the terms: 225 + -30d + d2 = 23 + 225 Combine like terms: 23 + 225 = 248 225 + -30d + d2 = 248 Factor a perfect square on the left side: (d + -15)(d + -15) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (d + -15) equal to 15.748015748 and -15.748015748.Subproblem 1
d + -15 = 15.748015748 Simplifying d + -15 = 15.748015748 Reorder the terms: -15 + d = 15.748015748 Solving -15 + d = 15.748015748 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + d = 15.748015748 + 15 Combine like terms: -15 + 15 = 0 0 + d = 15.748015748 + 15 d = 15.748015748 + 15 Combine like terms: 15.748015748 + 15 = 30.748015748 d = 30.748015748 Simplifying d = 30.748015748Subproblem 2
d + -15 = -15.748015748 Simplifying d + -15 = -15.748015748 Reorder the terms: -15 + d = -15.748015748 Solving -15 + d = -15.748015748 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + d = -15.748015748 + 15 Combine like terms: -15 + 15 = 0 0 + d = -15.748015748 + 15 d = -15.748015748 + 15 Combine like terms: -15.748015748 + 15 = -0.748015748 d = -0.748015748 Simplifying d = -0.748015748Solution
The solution to the problem is based on the solutions from the subproblems. d = {30.748015748, -0.748015748}
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