5d^2-7d-8=0

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Solution for 5d^2-7d-8=0 equation:


Simplifying
5d2 + -7d + -8 = 0

Reorder the terms:
-8 + -7d + 5d2 = 0

Solving
-8 + -7d + 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 + -1.4d + d2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1.4d + 1.6 + d2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1.4d + d2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1.4d + d2 = 0 + 1.6
-1.4d + d2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1.4d + d2 = 1.6

The d term is -1.4d.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4d + 0.49 + d2 = 1.6 + 0.49

Reorder the terms:
0.49 + -1.4d + d2 = 1.6 + 0.49

Combine like terms: 1.6 + 0.49 = 2.09
0.49 + -1.4d + d2 = 2.09

Factor a perfect square on the left side:
(d + -0.7)(d + -0.7) = 2.09

Calculate the square root of the right side: 1.445683229

Break this problem into two subproblems by setting 
(d + -0.7) equal to 1.445683229 and -1.445683229.

Subproblem 1

d + -0.7 = 1.445683229 Simplifying d + -0.7 = 1.445683229 Reorder the terms: -0.7 + d = 1.445683229 Solving -0.7 + d = 1.445683229 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + d = 1.445683229 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + d = 1.445683229 + 0.7 d = 1.445683229 + 0.7 Combine like terms: 1.445683229 + 0.7 = 2.145683229 d = 2.145683229 Simplifying d = 2.145683229

Subproblem 2

d + -0.7 = -1.445683229 Simplifying d + -0.7 = -1.445683229 Reorder the terms: -0.7 + d = -1.445683229 Solving -0.7 + d = -1.445683229 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + d = -1.445683229 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + d = -1.445683229 + 0.7 d = -1.445683229 + 0.7 Combine like terms: -1.445683229 + 0.7 = -0.745683229 d = -0.745683229 Simplifying d = -0.745683229

Solution

The solution to the problem is based on the solutions from the subproblems. d = {2.145683229, -0.745683229}

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