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Simplifying 26d(4 + -5d) = -67 (4 * 26d + -5d * 26d) = -67 (104d + -130d2) = -67 Solving 104d + -130d2 = -67 Solving for variable 'd'. Reorder the terms: 67 + 104d + -130d2 = -67 + 67 Combine like terms: -67 + 67 = 0 67 + 104d + -130d2 = 0 Begin completing the square. Divide all terms by -130 the coefficient of the squared term: Divide each side by '-130'. -0.5153846154 + -0.8d + d2 = 0.0 Move the constant term to the right: Add '0.5153846154' to each side of the equation. -0.5153846154 + -0.8d + 0.5153846154 + d2 = 0.0 + 0.5153846154 Reorder the terms: -0.5153846154 + 0.5153846154 + -0.8d + d2 = 0.0 + 0.5153846154 Combine like terms: -0.5153846154 + 0.5153846154 = 0.0000000000 0.0000000000 + -0.8d + d2 = 0.0 + 0.5153846154 -0.8d + d2 = 0.0 + 0.5153846154 Combine like terms: 0.0 + 0.5153846154 = 0.5153846154 -0.8d + d2 = 0.5153846154 The d term is -0.8d. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8d + 0.16 + d2 = 0.5153846154 + 0.16 Reorder the terms: 0.16 + -0.8d + d2 = 0.5153846154 + 0.16 Combine like terms: 0.5153846154 + 0.16 = 0.6753846154 0.16 + -0.8d + d2 = 0.6753846154 Factor a perfect square on the left side: (d + -0.4)(d + -0.4) = 0.6753846154 Calculate the square root of the right side: 0.821817872 Break this problem into two subproblems by setting (d + -0.4) equal to 0.821817872 and -0.821817872.Subproblem 1
d + -0.4 = 0.821817872 Simplifying d + -0.4 = 0.821817872 Reorder the terms: -0.4 + d = 0.821817872 Solving -0.4 + d = 0.821817872 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + d = 0.821817872 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + d = 0.821817872 + 0.4 d = 0.821817872 + 0.4 Combine like terms: 0.821817872 + 0.4 = 1.221817872 d = 1.221817872 Simplifying d = 1.221817872Subproblem 2
d + -0.4 = -0.821817872 Simplifying d + -0.4 = -0.821817872 Reorder the terms: -0.4 + d = -0.821817872 Solving -0.4 + d = -0.821817872 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + d = -0.821817872 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + d = -0.821817872 + 0.4 d = -0.821817872 + 0.4 Combine like terms: -0.821817872 + 0.4 = -0.421817872 d = -0.421817872 Simplifying d = -0.421817872Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.221817872, -0.421817872}
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