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Simplifying -2d2 + 28d = -38 Reorder the terms: 28d + -2d2 = -38 Solving 28d + -2d2 = -38 Solving for variable 'd'. Reorder the terms: 38 + 28d + -2d2 = -38 + 38 Combine like terms: -38 + 38 = 0 38 + 28d + -2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 14d + -1d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 14d + -1d2)' equal to zero and attempt to solve: Simplifying 19 + 14d + -1d2 = 0 Solving 19 + 14d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + -14d + d2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -14d + 19 + d2 = 0 + 19 Reorder the terms: -19 + 19 + -14d + d2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -14d + d2 = 0 + 19 -14d + d2 = 0 + 19 Combine like terms: 0 + 19 = 19 -14d + d2 = 19 The d term is -14d. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14d + 49 + d2 = 19 + 49 Reorder the terms: 49 + -14d + d2 = 19 + 49 Combine like terms: 19 + 49 = 68 49 + -14d + d2 = 68 Factor a perfect square on the left side: (d + -7)(d + -7) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (d + -7) equal to 8.246211251 and -8.246211251.Subproblem 1
d + -7 = 8.246211251 Simplifying d + -7 = 8.246211251 Reorder the terms: -7 + d = 8.246211251 Solving -7 + d = 8.246211251 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = 8.246211251 + 7 Combine like terms: -7 + 7 = 0 0 + d = 8.246211251 + 7 d = 8.246211251 + 7 Combine like terms: 8.246211251 + 7 = 15.246211251 d = 15.246211251 Simplifying d = 15.246211251Subproblem 2
d + -7 = -8.246211251 Simplifying d + -7 = -8.246211251 Reorder the terms: -7 + d = -8.246211251 Solving -7 + d = -8.246211251 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = -8.246211251 + 7 Combine like terms: -7 + 7 = 0 0 + d = -8.246211251 + 7 d = -8.246211251 + 7 Combine like terms: -8.246211251 + 7 = -1.246211251 d = -1.246211251 Simplifying d = -1.246211251Solution
The solution to the problem is based on the solutions from the subproblems. d = {15.246211251, -1.246211251}Solution
d = {15.246211251, -1.246211251}
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