d^2+0.7d-0.532=0

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Solution for d^2+0.7d-0.532=0 equation:


Simplifying
d2 + 0.7d + -0.532 = 0

Reorder the terms:
-0.532 + 0.7d + d2 = 0

Solving
-0.532 + 0.7d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '0.532' to each side of the equation.
-0.532 + 0.7d + 0.532 + d2 = 0 + 0.532

Reorder the terms:
-0.532 + 0.532 + 0.7d + d2 = 0 + 0.532

Combine like terms: -0.532 + 0.532 = 0.000
0.000 + 0.7d + d2 = 0 + 0.532
0.7d + d2 = 0 + 0.532

Combine like terms: 0 + 0.532 = 0.532
0.7d + d2 = 0.532

The d term is 0.7d.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7d + 0.1225 + d2 = 0.532 + 0.1225

Reorder the terms:
0.1225 + 0.7d + d2 = 0.532 + 0.1225

Combine like terms: 0.532 + 0.1225 = 0.6545
0.1225 + 0.7d + d2 = 0.6545

Factor a perfect square on the left side:
(d + 0.35)(d + 0.35) = 0.6545

Calculate the square root of the right side: 0.809011743

Break this problem into two subproblems by setting 
(d + 0.35) equal to 0.809011743 and -0.809011743.


Subproblem 1
d + 0.35 = 0.809011743

Simplifying
d + 0.35 = 0.809011743

Reorder the terms:
0.35 + d = 0.809011743

Solving
0.35 + d = 0.809011743

Solving for variable 'd'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + d = 0.809011743 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + d = 0.809011743 + -0.35
d = 0.809011743 + -0.35

Combine like terms: 0.809011743 + -0.35 = 0.459011743
d = 0.459011743

Simplifying
d = 0.459011743


Subproblem 2
d + 0.35 = -0.809011743

Simplifying
d + 0.35 = -0.809011743

Reorder the terms:
0.35 + d = -0.809011743

Solving
0.35 + d = -0.809011743

Solving for variable 'd'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + d = -0.809011743 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + d = -0.809011743 + -0.35
d = -0.809011743 + -0.35

Combine like terms: -0.809011743 + -0.35 = -1.159011743
d = -1.159011743

Simplifying
d = -1.159011743


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.459011743, -1.159011743}

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