(-a^2+1)-(a^2-2)+(5a^2-4a+8)=

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Solution for (-a^2+1)-(a^2-2)+(5a^2-4a+8)= equation: 


Simplifying
(-1a2 + 1) + -1(a2 + -2) + (5a2 + -4a + 8) = 0

Reorder the terms:
(1 + -1a2) + -1(a2 + -2) + (5a2 + -4a + 8) = 0

Remove parenthesis around (1 + -1a2)
1 + -1a2 + -1(a2 + -2) + (5a2 + -4a + 8) = 0

Reorder the terms:
1 + -1a2 + -1(-2 + a2) + (5a2 + -4a + 8) = 0
1 + -1a2 + (-2 * -1 + a2 * -1) + (5a2 + -4a + 8) = 0
1 + -1a2 + (2 + -1a2) + (5a2 + -4a + 8) = 0

Reorder the terms:
1 + -1a2 + 2 + -1a2 + (8 + -4a + 5a2) = 0

Remove parenthesis around (8 + -4a + 5a2)
1 + -1a2 + 2 + -1a2 + 8 + -4a + 5a2 = 0

Reorder the terms:
1 + 2 + 8 + -4a + -1a2 + -1a2 + 5a2 = 0

Combine like terms: 1 + 2 = 3
3 + 8 + -4a + -1a2 + -1a2 + 5a2 = 0

Combine like terms: 3 + 8 = 11
11 + -4a + -1a2 + -1a2 + 5a2 = 0

Combine like terms: -1a2 + -1a2 = -2a2
11 + -4a + -2a2 + 5a2 = 0

Combine like terms: -2a2 + 5a2 = 3a2
11 + -4a + 3a2 = 0

Solving
11 + -4a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
3.666666667 + -1.333333333a + a2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -1.333333333a + -3.666666667 + a2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -1.333333333a + a2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -1.333333333a + a2 = 0 + -3.666666667
-1.333333333a + a2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-1.333333333a + a2 = -3.666666667

The a term is -1.333333333a.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333a + 0.4444444442 + a2 = -3.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333a + a2 = -3.666666667 + 0.4444444442

Combine like terms: -3.666666667 + 0.4444444442 = -3.2222222228
0.4444444442 + -1.333333333a + a2 = -3.2222222228

Factor a perfect square on the left side:
(a + -0.6666666665)(a + -0.6666666665) = -3.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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