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Simplifying 9d2 + -7d + -8 = 0 Reorder the terms: -8 + -7d + 9d2 = 0 Solving -8 + -7d + 9d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -0.7777777778d + d2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.7777777778d + 0.8888888889 + d2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.7777777778d + d2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.7777777778d + d2 = 0 + 0.8888888889 -0.7777777778d + d2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.7777777778d + d2 = 0.8888888889 The d term is -0.7777777778d. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778d + 0.1512345679 + d2 = 0.8888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778d + d2 = 0.8888888889 + 0.1512345679 Combine like terms: 0.8888888889 + 0.1512345679 = 1.0401234568 0.1512345679 + -0.7777777778d + d2 = 1.0401234568 Factor a perfect square on the left side: (d + -0.3888888889)(d + -0.3888888889) = 1.0401234568 Calculate the square root of the right side: 1.019864431 Break this problem into two subproblems by setting (d + -0.3888888889) equal to 1.019864431 and -1.019864431.Subproblem 1
d + -0.3888888889 = 1.019864431 Simplifying d + -0.3888888889 = 1.019864431 Reorder the terms: -0.3888888889 + d = 1.019864431 Solving -0.3888888889 + d = 1.019864431 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + d = 1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + d = 1.019864431 + 0.3888888889 d = 1.019864431 + 0.3888888889 Combine like terms: 1.019864431 + 0.3888888889 = 1.4087533199 d = 1.4087533199 Simplifying d = 1.4087533199Subproblem 2
d + -0.3888888889 = -1.019864431 Simplifying d + -0.3888888889 = -1.019864431 Reorder the terms: -0.3888888889 + d = -1.019864431 Solving -0.3888888889 + d = -1.019864431 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + d = -1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + d = -1.019864431 + 0.3888888889 d = -1.019864431 + 0.3888888889 Combine like terms: -1.019864431 + 0.3888888889 = -0.6309755421 d = -0.6309755421 Simplifying d = -0.6309755421Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.4087533199, -0.6309755421}
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