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Simplifying 4d2 + -4d + -36 = 0 Reorder the terms: -36 + -4d + 4d2 = 0 Solving -36 + -4d + 4d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -1d + d2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -1d + d2)' equal to zero and attempt to solve: Simplifying -9 + -1d + d2 = 0 Solving -9 + -1d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -1d + 9 + d2 = 0 + 9 Reorder the terms: -9 + 9 + -1d + d2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1d + d2 = 0 + 9 -1d + d2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1d + d2 = 9 The d term is -1d. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1d + 0.25 + d2 = 9 + 0.25 Reorder the terms: 0.25 + -1d + d2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1d + d2 = 9.25 Factor a perfect square on the left side: (d + -0.5)(d + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (d + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
d + -0.5 = 3.041381265 Simplifying d + -0.5 = 3.041381265 Reorder the terms: -0.5 + d = 3.041381265 Solving -0.5 + d = 3.041381265 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = 3.041381265 + 0.5 d = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 d = 3.541381265 Simplifying d = 3.541381265Subproblem 2
d + -0.5 = -3.041381265 Simplifying d + -0.5 = -3.041381265 Reorder the terms: -0.5 + d = -3.041381265 Solving -0.5 + d = -3.041381265 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = -3.041381265 + 0.5 d = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 d = -2.541381265 Simplifying d = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.541381265, -2.541381265}Solution
d = {3.541381265, -2.541381265}
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