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Simplifying -1d(d + 4) + 7d + 2(9d + 1) = 0 Reorder the terms: -1d(4 + d) + 7d + 2(9d + 1) = 0 (4 * -1d + d * -1d) + 7d + 2(9d + 1) = 0 (-4d + -1d2) + 7d + 2(9d + 1) = 0 Reorder the terms: -4d + -1d2 + 7d + 2(1 + 9d) = 0 -4d + -1d2 + 7d + (1 * 2 + 9d * 2) = 0 -4d + -1d2 + 7d + (2 + 18d) = 0 Reorder the terms: 2 + -4d + 7d + 18d + -1d2 = 0 Combine like terms: -4d + 7d = 3d 2 + 3d + 18d + -1d2 = 0 Combine like terms: 3d + 18d = 21d 2 + 21d + -1d2 = 0 Solving 2 + 21d + -1d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -21d + d2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -21d + 2 + d2 = 0 + 2 Reorder the terms: -2 + 2 + -21d + d2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -21d + d2 = 0 + 2 -21d + d2 = 0 + 2 Combine like terms: 0 + 2 = 2 -21d + d2 = 2 The d term is -21d. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21d + 110.25 + d2 = 2 + 110.25 Reorder the terms: 110.25 + -21d + d2 = 2 + 110.25 Combine like terms: 2 + 110.25 = 112.25 110.25 + -21d + d2 = 112.25 Factor a perfect square on the left side: (d + -10.5)(d + -10.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (d + -10.5) equal to 10.59481005 and -10.59481005.Subproblem 1
d + -10.5 = 10.59481005 Simplifying d + -10.5 = 10.59481005 Reorder the terms: -10.5 + d = 10.59481005 Solving -10.5 + d = 10.59481005 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + d = 10.59481005 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + d = 10.59481005 + 10.5 d = 10.59481005 + 10.5 Combine like terms: 10.59481005 + 10.5 = 21.09481005 d = 21.09481005 Simplifying d = 21.09481005Subproblem 2
d + -10.5 = -10.59481005 Simplifying d + -10.5 = -10.59481005 Reorder the terms: -10.5 + d = -10.59481005 Solving -10.5 + d = -10.59481005 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + d = -10.59481005 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + d = -10.59481005 + 10.5 d = -10.59481005 + 10.5 Combine like terms: -10.59481005 + 10.5 = -0.09481005 d = -0.09481005 Simplifying d = -0.09481005Solution
The solution to the problem is based on the solutions from the subproblems. d = {21.09481005, -0.09481005}
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