3d^2+21d+45=-3

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Solution for 3d^2+21d+45=-3 equation:


Simplifying
3d2 + 21d + 45 = -3

Reorder the terms:
45 + 21d + 3d2 = -3

Solving
45 + 21d + 3d2 = -3

Solving for variable 'd'.

Reorder the terms:
45 + 3 + 21d + 3d2 = -3 + 3

Combine like terms: 45 + 3 = 48
48 + 21d + 3d2 = -3 + 3

Combine like terms: -3 + 3 = 0
48 + 21d + 3d2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 7d + d2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(16 + 7d + d2)' equal to zero and attempt to solve: Simplifying 16 + 7d + d2 = 0 Solving 16 + 7d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 7d + -16 + d2 = 0 + -16 Reorder the terms: 16 + -16 + 7d + d2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 7d + d2 = 0 + -16 7d + d2 = 0 + -16 Combine like terms: 0 + -16 = -16 7d + d2 = -16 The d term is 7d. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7d + 12.25 + d2 = -16 + 12.25 Reorder the terms: 12.25 + 7d + d2 = -16 + 12.25 Combine like terms: -16 + 12.25 = -3.75 12.25 + 7d + d2 = -3.75 Factor a perfect square on the left side: (d + 3.5)(d + 3.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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