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Simplifying 25d(d + -12) = 4 Reorder the terms: 25d(-12 + d) = 4 (-12 * 25d + d * 25d) = 4 (-300d + 25d2) = 4 Solving -300d + 25d2 = 4 Solving for variable 'd'. Reorder the terms: -4 + -300d + 25d2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -300d + 25d2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -12d + d2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -12d + 0.16 + d2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -12d + d2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -12d + d2 = 0 + 0.16 -12d + d2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -12d + d2 = 0.16 The d term is -12d. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12d + 36 + d2 = 0.16 + 36 Reorder the terms: 36 + -12d + d2 = 0.16 + 36 Combine like terms: 0.16 + 36 = 36.16 36 + -12d + d2 = 36.16 Factor a perfect square on the left side: (d + -6)(d + -6) = 36.16 Calculate the square root of the right side: 6.013318551 Break this problem into two subproblems by setting (d + -6) equal to 6.013318551 and -6.013318551.Subproblem 1
d + -6 = 6.013318551 Simplifying d + -6 = 6.013318551 Reorder the terms: -6 + d = 6.013318551 Solving -6 + d = 6.013318551 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = 6.013318551 + 6 Combine like terms: -6 + 6 = 0 0 + d = 6.013318551 + 6 d = 6.013318551 + 6 Combine like terms: 6.013318551 + 6 = 12.013318551 d = 12.013318551 Simplifying d = 12.013318551Subproblem 2
d + -6 = -6.013318551 Simplifying d + -6 = -6.013318551 Reorder the terms: -6 + d = -6.013318551 Solving -6 + d = -6.013318551 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = -6.013318551 + 6 Combine like terms: -6 + 6 = 0 0 + d = -6.013318551 + 6 d = -6.013318551 + 6 Combine like terms: -6.013318551 + 6 = -0.013318551 d = -0.013318551 Simplifying d = -0.013318551Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.013318551, -0.013318551}
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