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Simplifying -7d2 + -6d + -1 = 0 Reorder the terms: -1 + -6d + -7d2 = 0 Solving -1 + -6d + -7d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 6d + 7d2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 6d + 7d2)' equal to zero and attempt to solve: Simplifying 1 + 6d + 7d2 = 0 Solving 1 + 6d + 7d2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.8571428571d + d2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.8571428571d + -0.1428571429 + d2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.8571428571d + d2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.8571428571d + d2 = 0 + -0.1428571429 0.8571428571d + d2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.8571428571d + d2 = -0.1428571429 The d term is 0.8571428571d. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571d + 0.1836734694 + d2 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571d + d2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + 0.8571428571d + d2 = 0.0408163265 Factor a perfect square on the left side: (d + 0.4285714286)(d + 0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (d + 0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
d + 0.4285714286 = 0.202030509 Simplifying d + 0.4285714286 = 0.202030509 Reorder the terms: 0.4285714286 + d = 0.202030509 Solving 0.4285714286 + d = 0.202030509 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + d = 0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + d = 0.202030509 + -0.4285714286 d = 0.202030509 + -0.4285714286 Combine like terms: 0.202030509 + -0.4285714286 = -0.2265409196 d = -0.2265409196 Simplifying d = -0.2265409196Subproblem 2
d + 0.4285714286 = -0.202030509 Simplifying d + 0.4285714286 = -0.202030509 Reorder the terms: 0.4285714286 + d = -0.202030509 Solving 0.4285714286 + d = -0.202030509 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + d = -0.202030509 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + d = -0.202030509 + -0.4285714286 d = -0.202030509 + -0.4285714286 Combine like terms: -0.202030509 + -0.4285714286 = -0.6306019376 d = -0.6306019376 Simplifying d = -0.6306019376Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.2265409196, -0.6306019376}Solution
d = {-0.2265409196, -0.6306019376}
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