5d^2+6d-6=0

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Solution for 5d^2+6d-6=0 equation:


Simplifying
5d2 + 6d + -6 = 0

Reorder the terms:
-6 + 6d + 5d2 = 0

Solving
-6 + 6d + 5d2 = 0

Solving for variable 'd'.

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

Divide each side by '5'.
-1.2 + 1.2d + d2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.2d + 1.2 + d2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.2d + d2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.2d + d2 = 0 + 1.2
1.2d + d2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
1.2d + d2 = 1.2

The d term is 1.2d.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2d + 0.36 + d2 = 1.2 + 0.36

Reorder the terms:
0.36 + 1.2d + d2 = 1.2 + 0.36

Combine like terms: 1.2 + 0.36 = 1.56
0.36 + 1.2d + d2 = 1.56

Factor a perfect square on the left side:
(d + 0.6)(d + 0.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(d + 0.6) equal to 1.2489996 and -1.2489996.

Subproblem 1

d + 0.6 = 1.2489996 Simplifying d + 0.6 = 1.2489996 Reorder the terms: 0.6 + d = 1.2489996 Solving 0.6 + d = 1.2489996 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + d = 1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + d = 1.2489996 + -0.6 d = 1.2489996 + -0.6 Combine like terms: 1.2489996 + -0.6 = 0.6489996 d = 0.6489996 Simplifying d = 0.6489996

Subproblem 2

d + 0.6 = -1.2489996 Simplifying d + 0.6 = -1.2489996 Reorder the terms: 0.6 + d = -1.2489996 Solving 0.6 + d = -1.2489996 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + d = -1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + d = -1.2489996 + -0.6 d = -1.2489996 + -0.6 Combine like terms: -1.2489996 + -0.6 = -1.8489996 d = -1.8489996 Simplifying d = -1.8489996

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.6489996, -1.8489996}

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