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Simplifying 0.25d(d + -12) = 4 Reorder the terms: 0.25d(-12 + d) = 4 (-12 * 0.25d + d * 0.25d) = 4 (-3d + 0.25d2) = 4 Solving -3d + 0.25d2 = 4 Solving for variable 'd'. Reorder the terms: -4 + -3d + 0.25d2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -3d + 0.25d2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -16 + -12d + d2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -12d + 16 + d2 = 0 + 16 Reorder the terms: -16 + 16 + -12d + d2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -12d + d2 = 0 + 16 -12d + d2 = 0 + 16 Combine like terms: 0 + 16 = 16 -12d + d2 = 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 = 16 + 36 Reorder the terms: 36 + -12d + d2 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + -12d + d2 = 52 Factor a perfect square on the left side: (d + -6)(d + -6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (d + -6) equal to 7.211102551 and -7.211102551.Subproblem 1
d + -6 = 7.211102551 Simplifying d + -6 = 7.211102551 Reorder the terms: -6 + d = 7.211102551 Solving -6 + d = 7.211102551 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 = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + d = 7.211102551 + 6 d = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 d = 13.211102551 Simplifying d = 13.211102551Subproblem 2
d + -6 = -7.211102551 Simplifying d + -6 = -7.211102551 Reorder the terms: -6 + d = -7.211102551 Solving -6 + d = -7.211102551 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 = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + d = -7.211102551 + 6 d = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 d = -1.211102551 Simplifying d = -1.211102551Solution
The solution to the problem is based on the solutions from the subproblems. d = {13.211102551, -1.211102551}
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