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Simplifying 5d2 + -15d = 3 Reorder the terms: -15d + 5d2 = 3 Solving -15d + 5d2 = 3 Solving for variable 'd'. Reorder the terms: -3 + -15d + 5d2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -15d + 5d2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -3d + d2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3d + 0.6 + d2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3d + d2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3d + d2 = 0 + 0.6 -3d + d2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3d + d2 = 0.6 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = 0.6 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 0.6 + 2.25 Combine like terms: 0.6 + 2.25 = 2.85 2.25 + -3d + d2 = 2.85 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (d + -1.5) equal to 1.688194302 and -1.688194302.Subproblem 1
d + -1.5 = 1.688194302 Simplifying d + -1.5 = 1.688194302 Reorder the terms: -1.5 + d = 1.688194302 Solving -1.5 + d = 1.688194302 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = 1.688194302 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 1.688194302 + 1.5 d = 1.688194302 + 1.5 Combine like terms: 1.688194302 + 1.5 = 3.188194302 d = 3.188194302 Simplifying d = 3.188194302Subproblem 2
d + -1.5 = -1.688194302 Simplifying d + -1.5 = -1.688194302 Reorder the terms: -1.5 + d = -1.688194302 Solving -1.5 + d = -1.688194302 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = -1.688194302 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -1.688194302 + 1.5 d = -1.688194302 + 1.5 Combine like terms: -1.688194302 + 1.5 = -0.188194302 d = -0.188194302 Simplifying d = -0.188194302Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.188194302, -0.188194302}
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