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Simplifying 2d2 + 14d + -8 = 0 Reorder the terms: -8 + 14d + 2d2 = 0 Solving -8 + 14d + 2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 7d + d2)' equal to zero and attempt to solve: Simplifying -4 + 7d + d2 = 0 Solving -4 + 7d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 7d + 4 + d2 = 0 + 4 Reorder the terms: -4 + 4 + 7d + d2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7d + d2 = 0 + 4 7d + d2 = 0 + 4 Combine like terms: 0 + 4 = 4 7d + d2 = 4 The d term is 7d. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7d + 12.25 + d2 = 4 + 12.25 Reorder the terms: 12.25 + 7d + d2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7d + d2 = 16.25 Factor a perfect square on the left side: (d + 3.5)(d + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (d + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
d + 3.5 = 4.031128874 Simplifying d + 3.5 = 4.031128874 Reorder the terms: 3.5 + d = 4.031128874 Solving 3.5 + d = 4.031128874 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = 4.031128874 + -3.5 d = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 d = 0.531128874 Simplifying d = 0.531128874Subproblem 2
d + 3.5 = -4.031128874 Simplifying d + 3.5 = -4.031128874 Reorder the terms: 3.5 + d = -4.031128874 Solving 3.5 + d = -4.031128874 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = -4.031128874 + -3.5 d = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 d = -7.531128874 Simplifying d = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.531128874, -7.531128874}Solution
d = {0.531128874, -7.531128874}
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