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Simplifying -4d2 + -48d + 196 = 0 Reorder the terms: 196 + -48d + -4d2 = 0 Solving 196 + -48d + -4d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '4'. 4(49 + -12d + -1d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + -12d + -1d2)' equal to zero and attempt to solve: Simplifying 49 + -12d + -1d2 = 0 Solving 49 + -12d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 12d + d2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 12d + 49 + d2 = 0 + 49 Reorder the terms: -49 + 49 + 12d + d2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 12d + d2 = 0 + 49 12d + d2 = 0 + 49 Combine like terms: 0 + 49 = 49 12d + d2 = 49 The d term is 12d. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12d + 36 + d2 = 49 + 36 Reorder the terms: 36 + 12d + d2 = 49 + 36 Combine like terms: 49 + 36 = 85 36 + 12d + d2 = 85 Factor a perfect square on the left side: (d + 6)(d + 6) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (d + 6) equal to 9.219544457 and -9.219544457.Subproblem 1
d + 6 = 9.219544457 Simplifying d + 6 = 9.219544457 Reorder the terms: 6 + d = 9.219544457 Solving 6 + d = 9.219544457 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + d = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + d = 9.219544457 + -6 d = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 d = 3.219544457 Simplifying d = 3.219544457Subproblem 2
d + 6 = -9.219544457 Simplifying d + 6 = -9.219544457 Reorder the terms: 6 + d = -9.219544457 Solving 6 + d = -9.219544457 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + d = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + d = -9.219544457 + -6 d = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 d = -15.219544457 Simplifying d = -15.219544457Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.219544457, -15.219544457}Solution
d = {3.219544457, -15.219544457}
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