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Simplifying 4d2 + -7d + 1 = 0 Reorder the terms: 1 + -7d + 4d2 = 0 Solving 1 + -7d + 4d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -1.75d + d2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.75d + -0.25 + d2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.75d + d2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.75d + d2 = 0 + -0.25 -1.75d + d2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.75d + d2 = -0.25 The d term is -1.75d. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75d + 0.765625 + d2 = -0.25 + 0.765625 Reorder the terms: 0.765625 + -1.75d + d2 = -0.25 + 0.765625 Combine like terms: -0.25 + 0.765625 = 0.515625 0.765625 + -1.75d + d2 = 0.515625 Factor a perfect square on the left side: (d + -0.875)(d + -0.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (d + -0.875) equal to 0.718070331 and -0.718070331.Subproblem 1
d + -0.875 = 0.718070331 Simplifying d + -0.875 = 0.718070331 Reorder the terms: -0.875 + d = 0.718070331 Solving -0.875 + d = 0.718070331 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + d = 0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + d = 0.718070331 + 0.875 d = 0.718070331 + 0.875 Combine like terms: 0.718070331 + 0.875 = 1.593070331 d = 1.593070331 Simplifying d = 1.593070331Subproblem 2
d + -0.875 = -0.718070331 Simplifying d + -0.875 = -0.718070331 Reorder the terms: -0.875 + d = -0.718070331 Solving -0.875 + d = -0.718070331 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + d = -0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + d = -0.718070331 + 0.875 d = -0.718070331 + 0.875 Combine like terms: -0.718070331 + 0.875 = 0.156929669 d = 0.156929669 Simplifying d = 0.156929669Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.593070331, 0.156929669}
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