2d^2+52d+30=0

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Solution for 2d^2+52d+30=0 equation: 


Simplifying
2d2 + 52d + 30 = 0

Reorder the terms:
30 + 52d + 2d2 = 0

Solving
30 + 52d + 2d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 26d + d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 26d + d2)' equal to zero and attempt to solve:

Simplifying
15 + 26d + d2 = 0

Solving
15 + 26d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 26d + -15 + d2 = 0 + -15

Reorder the terms:
15 + -15 + 26d + d2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 26d + d2 = 0 + -15
26d + d2 = 0 + -15

Combine like terms: 0 + -15 = -15
26d + d2 = -15

The d term is 26d.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26d + 169 + d2 = -15 + 169

Reorder the terms:
169 + 26d + d2 = -15 + 169

Combine like terms: -15 + 169 = 154
169 + 26d + d2 = 154

Factor a perfect square on the left side:
(d + 13)(d + 13) = 154

Calculate the square root of the right side: 12.409673646

Break this problem into two subproblems by setting 
(d + 13) equal to 12.409673646 and -12.409673646.


Subproblem 1
d + 13 = 12.409673646

Simplifying
d + 13 = 12.409673646

Reorder the terms:
13 + d = 12.409673646

Solving
13 + d = 12.409673646

Solving for variable 'd'.

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

Add '-13' to each side of the equation.
13 + -13 + d = 12.409673646 + -13

Combine like terms: 13 + -13 = 0
0 + d = 12.409673646 + -13
d = 12.409673646 + -13

Combine like terms: 12.409673646 + -13 = -0.590326354
d = -0.590326354

Simplifying
d = -0.590326354


Subproblem 2
d + 13 = -12.409673646

Simplifying
d + 13 = -12.409673646

Reorder the terms:
13 + d = -12.409673646

Solving
13 + d = -12.409673646

Solving for variable 'd'.

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

Add '-13' to each side of the equation.
13 + -13 + d = -12.409673646 + -13

Combine like terms: 13 + -13 = 0
0 + d = -12.409673646 + -13
d = -12.409673646 + -13

Combine like terms: -12.409673646 + -13 = -25.409673646
d = -25.409673646

Simplifying
d = -25.409673646


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.590326354, -25.409673646}
Solution
d = {-0.590326354, -25.409673646}

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