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Simplifying 5d2 + 6d + -9 = 0 Reorder the terms: -9 + 6d + 5d2 = 0 Solving -9 + 6d + 5d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 1.2d + d2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 1.2d + 1.8 + d2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 1.2d + d2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 1.2d + d2 = 0 + 1.8 1.2d + d2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 1.2d + d2 = 1.8 The d term is 1.2d. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2d + 0.36 + d2 = 1.8 + 0.36 Reorder the terms: 0.36 + 1.2d + d2 = 1.8 + 0.36 Combine like terms: 1.8 + 0.36 = 2.16 0.36 + 1.2d + d2 = 2.16 Factor a perfect square on the left side: (d + 0.6)(d + 0.6) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (d + 0.6) equal to 1.469693846 and -1.469693846.Subproblem 1
d + 0.6 = 1.469693846 Simplifying d + 0.6 = 1.469693846 Reorder the terms: 0.6 + d = 1.469693846 Solving 0.6 + d = 1.469693846 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + d = 1.469693846 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + d = 1.469693846 + -0.6 d = 1.469693846 + -0.6 Combine like terms: 1.469693846 + -0.6 = 0.869693846 d = 0.869693846 Simplifying d = 0.869693846Subproblem 2
d + 0.6 = -1.469693846 Simplifying d + 0.6 = -1.469693846 Reorder the terms: 0.6 + d = -1.469693846 Solving 0.6 + d = -1.469693846 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + d = -1.469693846 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + d = -1.469693846 + -0.6 d = -1.469693846 + -0.6 Combine like terms: -1.469693846 + -0.6 = -2.069693846 d = -2.069693846 Simplifying d = -2.069693846Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.869693846, -2.069693846}
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