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Simplifying -9d2 + -5d + 6 = 0 Reorder the terms: 6 + -5d + -9d2 = 0 Solving 6 + -5d + -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'. -0.6666666667 + 0.5555555556d + d2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.5555555556d + 0.6666666667 + d2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.5555555556d + d2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.5555555556d + d2 = 0 + 0.6666666667 0.5555555556d + d2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.5555555556d + d2 = 0.6666666667 The d term is 0.5555555556d. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556d + 0.07716049384 + d2 = 0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556d + d2 = 0.6666666667 + 0.07716049384 Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054 0.07716049384 + 0.5555555556d + d2 = 0.74382716054 Factor a perfect square on the left side: (d + 0.2777777778)(d + 0.2777777778) = 0.74382716054 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting (d + 0.2777777778) equal to 0.86245415 and -0.86245415.Subproblem 1
d + 0.2777777778 = 0.86245415 Simplifying d + 0.2777777778 = 0.86245415 Reorder the terms: 0.2777777778 + d = 0.86245415 Solving 0.2777777778 + d = 0.86245415 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + d = 0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + d = 0.86245415 + -0.2777777778 d = 0.86245415 + -0.2777777778 Combine like terms: 0.86245415 + -0.2777777778 = 0.5846763722 d = 0.5846763722 Simplifying d = 0.5846763722Subproblem 2
d + 0.2777777778 = -0.86245415 Simplifying d + 0.2777777778 = -0.86245415 Reorder the terms: 0.2777777778 + d = -0.86245415 Solving 0.2777777778 + d = -0.86245415 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + d = -0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + d = -0.86245415 + -0.2777777778 d = -0.86245415 + -0.2777777778 Combine like terms: -0.86245415 + -0.2777777778 = -1.1402319278 d = -1.1402319278 Simplifying d = -1.1402319278Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.5846763722, -1.1402319278}
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