8a^2-9a-9=4-3a

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Solution for 8a^2-9a-9=4-3a equation:


Simplifying
8a2 + -9a + -9 = 4 + -3a

Reorder the terms:
-9 + -9a + 8a2 = 4 + -3a

Solving
-9 + -9a + 8a2 = 4 + -3a

Solving for variable 'a'.

Reorder the terms:
-9 + -4 + -9a + 3a + 8a2 = 4 + -3a + -4 + 3a

Combine like terms: -9 + -4 = -13
-13 + -9a + 3a + 8a2 = 4 + -3a + -4 + 3a

Combine like terms: -9a + 3a = -6a
-13 + -6a + 8a2 = 4 + -3a + -4 + 3a

Reorder the terms:
-13 + -6a + 8a2 = 4 + -4 + -3a + 3a

Combine like terms: 4 + -4 = 0
-13 + -6a + 8a2 = 0 + -3a + 3a
-13 + -6a + 8a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
-13 + -6a + 8a2 = 0

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

Divide each side by '8'.
-1.625 + -0.75a + a2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -0.75a + 1.625 + a2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -0.75a + a2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -0.75a + a2 = 0 + 1.625
-0.75a + a2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-0.75a + a2 = 1.625

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 = 1.625 + 0.140625

Reorder the terms:
0.140625 + -0.75a + a2 = 1.625 + 0.140625

Combine like terms: 1.625 + 0.140625 = 1.765625
0.140625 + -0.75a + a2 = 1.765625

Factor a perfect square on the left side:
(a + -0.375)(a + -0.375) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(a + -0.375) equal to 1.328768227 and -1.328768227.

Subproblem 1

a + -0.375 = 1.328768227 Simplifying a + -0.375 = 1.328768227 Reorder the terms: -0.375 + a = 1.328768227 Solving -0.375 + a = 1.328768227 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 = 1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 1.328768227 + 0.375 a = 1.328768227 + 0.375 Combine like terms: 1.328768227 + 0.375 = 1.703768227 a = 1.703768227 Simplifying a = 1.703768227

Subproblem 2

a + -0.375 = -1.328768227 Simplifying a + -0.375 = -1.328768227 Reorder the terms: -0.375 + a = -1.328768227 Solving -0.375 + a = -1.328768227 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 = -1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -1.328768227 + 0.375 a = -1.328768227 + 0.375 Combine like terms: -1.328768227 + 0.375 = -0.953768227 a = -0.953768227 Simplifying a = -0.953768227

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.703768227, -0.953768227}

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