d^2-9d+9=-4

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Solution for d^2-9d+9=-4 equation:


Simplifying
d2 + -9d + 9 = -4

Reorder the terms:
9 + -9d + d2 = -4

Solving
9 + -9d + d2 = -4

Solving for variable 'd'.

Reorder the terms:
9 + 4 + -9d + d2 = -4 + 4

Combine like terms: 9 + 4 = 13
13 + -9d + d2 = -4 + 4

Combine like terms: -4 + 4 = 0
13 + -9d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -9d + -13 + d2 = 0 + -13

Reorder the terms:
13 + -13 + -9d + d2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -9d + d2 = 0 + -13
-9d + d2 = 0 + -13

Combine like terms: 0 + -13 = -13
-9d + d2 = -13

The d term is -9d.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9d + 20.25 + d2 = -13 + 20.25

Reorder the terms:
20.25 + -9d + d2 = -13 + 20.25

Combine like terms: -13 + 20.25 = 7.25
20.25 + -9d + d2 = 7.25

Factor a perfect square on the left side:
(d + -4.5)(d + -4.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(d + -4.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

d + -4.5 = 2.692582404 Simplifying d + -4.5 = 2.692582404 Reorder the terms: -4.5 + d = 2.692582404 Solving -4.5 + d = 2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + d = 2.692582404 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = 2.692582404 + 4.5 d = 2.692582404 + 4.5 Combine like terms: 2.692582404 + 4.5 = 7.192582404 d = 7.192582404 Simplifying d = 7.192582404

Subproblem 2

d + -4.5 = -2.692582404 Simplifying d + -4.5 = -2.692582404 Reorder the terms: -4.5 + d = -2.692582404 Solving -4.5 + d = -2.692582404 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + d = -2.692582404 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = -2.692582404 + 4.5 d = -2.692582404 + 4.5 Combine like terms: -2.692582404 + 4.5 = 1.807417596 d = 1.807417596 Simplifying d = 1.807417596

Solution

The solution to the problem is based on the solutions from the subproblems. d = {7.192582404, 1.807417596}

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