20d^2+23d-23=0

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Solution for 20d^2+23d-23=0 equation:


Simplifying
20d2 + 23d + -23 = 0

Reorder the terms:
-23 + 23d + 20d2 = 0

Solving
-23 + 23d + 20d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
20 the coefficient of the squared term: 

Divide each side by '20'.
-1.15 + 1.15d + d2 = 0

Move the constant term to the right:

Add '1.15' to each side of the equation.
-1.15 + 1.15d + 1.15 + d2 = 0 + 1.15

Reorder the terms:
-1.15 + 1.15 + 1.15d + d2 = 0 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + 1.15d + d2 = 0 + 1.15
1.15d + d2 = 0 + 1.15

Combine like terms: 0 + 1.15 = 1.15
1.15d + d2 = 1.15

The d term is 1.15d.  Take half its coefficient (0.575).
Square it (0.330625) and add it to both sides.

Add '0.330625' to each side of the equation.
1.15d + 0.330625 + d2 = 1.15 + 0.330625

Reorder the terms:
0.330625 + 1.15d + d2 = 1.15 + 0.330625

Combine like terms: 1.15 + 0.330625 = 1.480625
0.330625 + 1.15d + d2 = 1.480625

Factor a perfect square on the left side:
(d + 0.575)(d + 0.575) = 1.480625

Calculate the square root of the right side: 1.216809352

Break this problem into two subproblems by setting 
(d + 0.575) equal to 1.216809352 and -1.216809352.

Subproblem 1

d + 0.575 = 1.216809352 Simplifying d + 0.575 = 1.216809352 Reorder the terms: 0.575 + d = 1.216809352 Solving 0.575 + d = 1.216809352 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + d = 1.216809352 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + d = 1.216809352 + -0.575 d = 1.216809352 + -0.575 Combine like terms: 1.216809352 + -0.575 = 0.641809352 d = 0.641809352 Simplifying d = 0.641809352

Subproblem 2

d + 0.575 = -1.216809352 Simplifying d + 0.575 = -1.216809352 Reorder the terms: 0.575 + d = -1.216809352 Solving 0.575 + d = -1.216809352 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + d = -1.216809352 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + d = -1.216809352 + -0.575 d = -1.216809352 + -0.575 Combine like terms: -1.216809352 + -0.575 = -1.791809352 d = -1.791809352 Simplifying d = -1.791809352

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.641809352, -1.791809352}

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