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Simplifying 9d2 + -13d + -10 = 10 Reorder the terms: -10 + -13d + 9d2 = 10 Solving -10 + -13d + 9d2 = 10 Solving for variable 'd'. Reorder the terms: -10 + -10 + -13d + 9d2 = 10 + -10 Combine like terms: -10 + -10 = -20 -20 + -13d + 9d2 = 10 + -10 Combine like terms: 10 + -10 = 0 -20 + -13d + 9d2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -1.444444444d + d2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -1.444444444d + 2.222222222 + d2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -1.444444444d + d2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -1.444444444d + d2 = 0 + 2.222222222 -1.444444444d + d2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -1.444444444d + d2 = 2.222222222 The d term is -1.444444444d. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444d + 0.5216049380 + d2 = 2.222222222 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444d + d2 = 2.222222222 + 0.5216049380 Combine like terms: 2.222222222 + 0.5216049380 = 2.74382716 0.5216049380 + -1.444444444d + d2 = 2.74382716 Factor a perfect square on the left side: (d + -0.722222222)(d + -0.722222222) = 2.74382716 Calculate the square root of the right side: 1.656450168 Break this problem into two subproblems by setting (d + -0.722222222) equal to 1.656450168 and -1.656450168.Subproblem 1
d + -0.722222222 = 1.656450168 Simplifying d + -0.722222222 = 1.656450168 Reorder the terms: -0.722222222 + d = 1.656450168 Solving -0.722222222 + d = 1.656450168 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + d = 1.656450168 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + d = 1.656450168 + 0.722222222 d = 1.656450168 + 0.722222222 Combine like terms: 1.656450168 + 0.722222222 = 2.37867239 d = 2.37867239 Simplifying d = 2.37867239Subproblem 2
d + -0.722222222 = -1.656450168 Simplifying d + -0.722222222 = -1.656450168 Reorder the terms: -0.722222222 + d = -1.656450168 Solving -0.722222222 + d = -1.656450168 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + d = -1.656450168 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + d = -1.656450168 + 0.722222222 d = -1.656450168 + 0.722222222 Combine like terms: -1.656450168 + 0.722222222 = -0.934227946 d = -0.934227946 Simplifying d = -0.934227946Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.37867239, -0.934227946}
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