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Simplifying 2d2 + -10d = 8 Reorder the terms: -10d + 2d2 = 8 Solving -10d + 2d2 = 8 Solving for variable 'd'. Reorder the terms: -8 + -10d + 2d2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -10d + 2d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -5d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5d + d2)' equal to zero and attempt to solve: Simplifying -4 + -5d + d2 = 0 Solving -4 + -5d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5d + 4 + d2 = 0 + 4 Reorder the terms: -4 + 4 + -5d + d2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5d + d2 = 0 + 4 -5d + d2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5d + d2 = 4 The d term is -5d. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5d + 6.25 + d2 = 4 + 6.25 Reorder the terms: 6.25 + -5d + d2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5d + d2 = 10.25 Factor a perfect square on the left side: (d + -2.5)(d + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (d + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
d + -2.5 = 3.201562119 Simplifying d + -2.5 = 3.201562119 Reorder the terms: -2.5 + d = 3.201562119 Solving -2.5 + d = 3.201562119 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = 3.201562119 + 2.5 d = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 d = 5.701562119 Simplifying d = 5.701562119Subproblem 2
d + -2.5 = -3.201562119 Simplifying d + -2.5 = -3.201562119 Reorder the terms: -2.5 + d = -3.201562119 Solving -2.5 + d = -3.201562119 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = -3.201562119 + 2.5 d = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 d = -0.701562119 Simplifying d = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.701562119, -0.701562119}Solution
d = {5.701562119, -0.701562119}
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