2d^2-28d+58=0

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Solution for 2d^2-28d+58=0 equation: 


Simplifying
2d2 + -28d + 58 = 0

Reorder the terms:
58 + -28d + 2d2 = 0

Solving
58 + -28d + 2d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -14d + d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(29 + -14d + d2)' equal to zero and attempt to solve:

Simplifying
29 + -14d + d2 = 0

Solving
29 + -14d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -14d + -29 + d2 = 0 + -29

Reorder the terms:
29 + -29 + -14d + d2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -14d + d2 = 0 + -29
-14d + d2 = 0 + -29

Combine like terms: 0 + -29 = -29
-14d + d2 = -29

The d term is -14d.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14d + 49 + d2 = -29 + 49

Reorder the terms:
49 + -14d + d2 = -29 + 49

Combine like terms: -29 + 49 = 20
49 + -14d + d2 = 20

Factor a perfect square on the left side:
(d + -7)(d + -7) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(d + -7) equal to 4.472135955 and -4.472135955.


Subproblem 1
d + -7 = 4.472135955

Simplifying
d + -7 = 4.472135955

Reorder the terms:
-7 + d = 4.472135955

Solving
-7 + d = 4.472135955

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + d = 4.472135955 + 7

Combine like terms: -7 + 7 = 0
0 + d = 4.472135955 + 7
d = 4.472135955 + 7

Combine like terms: 4.472135955 + 7 = 11.472135955
d = 11.472135955

Simplifying
d = 11.472135955


Subproblem 2
d + -7 = -4.472135955

Simplifying
d + -7 = -4.472135955

Reorder the terms:
-7 + d = -4.472135955

Solving
-7 + d = -4.472135955

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + d = -4.472135955 + 7

Combine like terms: -7 + 7 = 0
0 + d = -4.472135955 + 7
d = -4.472135955 + 7

Combine like terms: -4.472135955 + 7 = 2.527864045
d = 2.527864045

Simplifying
d = 2.527864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {11.472135955, 2.527864045}
Solution
d = {11.472135955, 2.527864045}

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