8a^2-6a-3=0

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Solution for 8a^2-6a-3=0 equation:


Simplifying
8a2 + -6a + -3 = 0

Reorder the terms:
-3 + -6a + 8a2 = 0

Solving
-3 + -6a + 8a2 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-0.375 + -0.75a + a2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.75a + 0.375 + a2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.75a + a2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.75a + a2 = 0 + 0.375
-0.75a + a2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.75a + a2 = 0.375

The a term is -0.75a.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75a + 0.140625 + a2 = 0.375 + 0.140625

Reorder the terms:
0.140625 + -0.75a + a2 = 0.375 + 0.140625

Combine like terms: 0.375 + 0.140625 = 0.515625
0.140625 + -0.75a + a2 = 0.515625

Factor a perfect square on the left side:
(a + -0.375)(a + -0.375) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(a + -0.375) equal to 0.718070331 and -0.718070331.

Subproblem 1

a + -0.375 = 0.718070331 Simplifying a + -0.375 = 0.718070331 Reorder the terms: -0.375 + a = 0.718070331 Solving -0.375 + a = 0.718070331 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = 0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 0.718070331 + 0.375 a = 0.718070331 + 0.375 Combine like terms: 0.718070331 + 0.375 = 1.093070331 a = 1.093070331 Simplifying a = 1.093070331

Subproblem 2

a + -0.375 = -0.718070331 Simplifying a + -0.375 = -0.718070331 Reorder the terms: -0.375 + a = -0.718070331 Solving -0.375 + a = -0.718070331 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = -0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -0.718070331 + 0.375 a = -0.718070331 + 0.375 Combine like terms: -0.718070331 + 0.375 = -0.343070331 a = -0.343070331 Simplifying a = -0.343070331

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.093070331, -0.343070331}

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