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Simplifying d(d + 5) = 3(d + -3) + 6d Reorder the terms: d(5 + d) = 3(d + -3) + 6d (5 * d + d * d) = 3(d + -3) + 6d (5d + d2) = 3(d + -3) + 6d Reorder the terms: 5d + d2 = 3(-3 + d) + 6d 5d + d2 = (-3 * 3 + d * 3) + 6d 5d + d2 = (-9 + 3d) + 6d Combine like terms: 3d + 6d = 9d 5d + d2 = -9 + 9d Solving 5d + d2 = -9 + 9d Solving for variable 'd'. Reorder the terms: 9 + 5d + -9d + d2 = -9 + 9d + 9 + -9d Combine like terms: 5d + -9d = -4d 9 + -4d + d2 = -9 + 9d + 9 + -9d Reorder the terms: 9 + -4d + d2 = -9 + 9 + 9d + -9d Combine like terms: -9 + 9 = 0 9 + -4d + d2 = 0 + 9d + -9d 9 + -4d + d2 = 9d + -9d Combine like terms: 9d + -9d = 0 9 + -4d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -4d + -9 + d2 = 0 + -9 Reorder the terms: 9 + -9 + -4d + d2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4d + d2 = 0 + -9 -4d + d2 = 0 + -9 Combine like terms: 0 + -9 = -9 -4d + d2 = -9 The d term is -4d. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4d + 4 + d2 = -9 + 4 Reorder the terms: 4 + -4d + d2 = -9 + 4 Combine like terms: -9 + 4 = -5 4 + -4d + d2 = -5 Factor a perfect square on the left side: (d + -2)(d + -2) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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