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Simplifying 18d2 + 4d = 10 Reorder the terms: 4d + 18d2 = 10 Solving 4d + 18d2 = 10 Solving for variable 'd'. Reorder the terms: -10 + 4d + 18d2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 4d + 18d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 2d + 9d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 2d + 9d2)' equal to zero and attempt to solve: Simplifying -5 + 2d + 9d2 = 0 Solving -5 + 2d + 9d2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.2222222222d + d2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.2222222222d + 0.5555555556 + d2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.2222222222d + d2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.2222222222d + d2 = 0 + 0.5555555556 0.2222222222d + d2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.2222222222d + d2 = 0.5555555556 The d term is 0.2222222222d. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222d + 0.01234567901 + d2 = 0.5555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222d + d2 = 0.5555555556 + 0.01234567901 Combine like terms: 0.5555555556 + 0.01234567901 = 0.56790123461 0.01234567901 + 0.2222222222d + d2 = 0.56790123461 Factor a perfect square on the left side: (d + 0.1111111111)(d + 0.1111111111) = 0.56790123461 Calculate the square root of the right side: 0.75359222 Break this problem into two subproblems by setting (d + 0.1111111111) equal to 0.75359222 and -0.75359222.Subproblem 1
d + 0.1111111111 = 0.75359222 Simplifying d + 0.1111111111 = 0.75359222 Reorder the terms: 0.1111111111 + d = 0.75359222 Solving 0.1111111111 + d = 0.75359222 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + d = 0.75359222 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + d = 0.75359222 + -0.1111111111 d = 0.75359222 + -0.1111111111 Combine like terms: 0.75359222 + -0.1111111111 = 0.6424811089 d = 0.6424811089 Simplifying d = 0.6424811089Subproblem 2
d + 0.1111111111 = -0.75359222 Simplifying d + 0.1111111111 = -0.75359222 Reorder the terms: 0.1111111111 + d = -0.75359222 Solving 0.1111111111 + d = -0.75359222 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + d = -0.75359222 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + d = -0.75359222 + -0.1111111111 d = -0.75359222 + -0.1111111111 Combine like terms: -0.75359222 + -0.1111111111 = -0.8647033311 d = -0.8647033311 Simplifying d = -0.8647033311Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.6424811089, -0.8647033311}Solution
d = {0.6424811089, -0.8647033311}
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