5d^2-2d-8=0

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Solution for 5d^2-2d-8=0 equation:


Simplifying
5d2 + -2d + -8 = 0

Reorder the terms:
-8 + -2d + 5d2 = 0

Solving
-8 + -2d + 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'.
-1.6 + -0.4d + d2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.4d + 1.6 + d2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.4d + d2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.4d + d2 = 0 + 1.6
-0.4d + d2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.4d + d2 = 1.6

The d term is -0.4d.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4d + 0.04 + d2 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4d + d2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4d + d2 = 1.64

Factor a perfect square on the left side:
(d + -0.2)(d + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(d + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1

d + -0.2 = 1.280624847 Simplifying d + -0.2 = 1.280624847 Reorder the terms: -0.2 + d = 1.280624847 Solving -0.2 + d = 1.280624847 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + d = 1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + d = 1.280624847 + 0.2 d = 1.280624847 + 0.2 Combine like terms: 1.280624847 + 0.2 = 1.480624847 d = 1.480624847 Simplifying d = 1.480624847

Subproblem 2

d + -0.2 = -1.280624847 Simplifying d + -0.2 = -1.280624847 Reorder the terms: -0.2 + d = -1.280624847 Solving -0.2 + d = -1.280624847 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + d = -1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + d = -1.280624847 + 0.2 d = -1.280624847 + 0.2 Combine like terms: -1.280624847 + 0.2 = -1.080624847 d = -1.080624847 Simplifying d = -1.080624847

Solution

The solution to the problem is based on the solutions from the subproblems. d = {1.480624847, -1.080624847}

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