8*a^2+3a-800=0

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Solution for 8*a^2+3a-800=0 equation:


Simplifying
8a2 + 3a + -800 = 0

Reorder the terms:
-800 + 3a + 8a2 = 0

Solving
-800 + 3a + 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'.
-100 + 0.375a + a2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 0.375a + 100 + a2 = 0 + 100

Reorder the terms:
-100 + 100 + 0.375a + a2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 0.375a + a2 = 0 + 100
0.375a + a2 = 0 + 100

Combine like terms: 0 + 100 = 100
0.375a + a2 = 100

The a term is 0.375a.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375a + 0.03515625 + a2 = 100 + 0.03515625

Reorder the terms:
0.03515625 + 0.375a + a2 = 100 + 0.03515625

Combine like terms: 100 + 0.03515625 = 100.03515625
0.03515625 + 0.375a + a2 = 100.03515625

Factor a perfect square on the left side:
(a + 0.1875)(a + 0.1875) = 100.03515625

Calculate the square root of the right side: 10.001757658

Break this problem into two subproblems by setting 
(a + 0.1875) equal to 10.001757658 and -10.001757658.

Subproblem 1

a + 0.1875 = 10.001757658 Simplifying a + 0.1875 = 10.001757658 Reorder the terms: 0.1875 + a = 10.001757658 Solving 0.1875 + a = 10.001757658 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = 10.001757658 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = 10.001757658 + -0.1875 a = 10.001757658 + -0.1875 Combine like terms: 10.001757658 + -0.1875 = 9.814257658 a = 9.814257658 Simplifying a = 9.814257658

Subproblem 2

a + 0.1875 = -10.001757658 Simplifying a + 0.1875 = -10.001757658 Reorder the terms: 0.1875 + a = -10.001757658 Solving 0.1875 + a = -10.001757658 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = -10.001757658 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = -10.001757658 + -0.1875 a = -10.001757658 + -0.1875 Combine like terms: -10.001757658 + -0.1875 = -10.189257658 a = -10.189257658 Simplifying a = -10.189257658

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.814257658, -10.189257658}

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