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Simplifying -2d2 + -10d + 98 = 0 Reorder the terms: 98 + -10d + -2d2 = 0 Solving 98 + -10d + -2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -5d + -1d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + -5d + -1d2)' equal to zero and attempt to solve: Simplifying 49 + -5d + -1d2 = 0 Solving 49 + -5d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 5d + d2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 5d + 49 + d2 = 0 + 49 Reorder the terms: -49 + 49 + 5d + d2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 5d + d2 = 0 + 49 5d + d2 = 0 + 49 Combine like terms: 0 + 49 = 49 5d + d2 = 49 The d term is 5d. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5d + 6.25 + d2 = 49 + 6.25 Reorder the terms: 6.25 + 5d + d2 = 49 + 6.25 Combine like terms: 49 + 6.25 = 55.25 6.25 + 5d + d2 = 55.25 Factor a perfect square on the left side: (d + 2.5)(d + 2.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (d + 2.5) equal to 7.433034374 and -7.433034374.Subproblem 1
d + 2.5 = 7.433034374 Simplifying d + 2.5 = 7.433034374 Reorder the terms: 2.5 + d = 7.433034374 Solving 2.5 + d = 7.433034374 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + d = 7.433034374 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + d = 7.433034374 + -2.5 d = 7.433034374 + -2.5 Combine like terms: 7.433034374 + -2.5 = 4.933034374 d = 4.933034374 Simplifying d = 4.933034374Subproblem 2
d + 2.5 = -7.433034374 Simplifying d + 2.5 = -7.433034374 Reorder the terms: 2.5 + d = -7.433034374 Solving 2.5 + d = -7.433034374 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + d = -7.433034374 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + d = -7.433034374 + -2.5 d = -7.433034374 + -2.5 Combine like terms: -7.433034374 + -2.5 = -9.933034374 d = -9.933034374 Simplifying d = -9.933034374Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.933034374, -9.933034374}Solution
d = {4.933034374, -9.933034374}
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