d^2+3d-28=d

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Solution for d^2+3d-28=d equation:


Simplifying
d2 + 3d + -28 = d

Reorder the terms:
-28 + 3d + d2 = d

Solving
-28 + 3d + d2 = d

Solving for variable 'd'.

Reorder the terms:
-28 + 3d + -1d + d2 = d + -1d

Combine like terms: 3d + -1d = 2d
-28 + 2d + d2 = d + -1d

Combine like terms: d + -1d = 0
-28 + 2d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2d + 28 + d2 = 0 + 28

Reorder the terms:
-28 + 28 + 2d + d2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2d + d2 = 0 + 28
2d + d2 = 0 + 28

Combine like terms: 0 + 28 = 28
2d + d2 = 28

The d term is 2d.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2d + 1 + d2 = 28 + 1

Reorder the terms:
1 + 2d + d2 = 28 + 1

Combine like terms: 28 + 1 = 29
1 + 2d + d2 = 29

Factor a perfect square on the left side:
(d + 1)(d + 1) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(d + 1) equal to 5.385164807 and -5.385164807.

Subproblem 1

d + 1 = 5.385164807 Simplifying d + 1 = 5.385164807 Reorder the terms: 1 + d = 5.385164807 Solving 1 + d = 5.385164807 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + d = 5.385164807 + -1 d = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 d = 4.385164807 Simplifying d = 4.385164807

Subproblem 2

d + 1 = -5.385164807 Simplifying d + 1 = -5.385164807 Reorder the terms: 1 + d = -5.385164807 Solving 1 + d = -5.385164807 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + d = -5.385164807 + -1 d = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 d = -6.385164807 Simplifying d = -6.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. d = {4.385164807, -6.385164807}

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