11+-4a=-7a(a+-1)+1

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Solution for 11+-4a=-7a(a+-1)+1 equation: 


Simplifying
11 + -4a = -7a(a + -1) + 1

Reorder the terms:
11 + -4a = -7a(-1 + a) + 1
11 + -4a = (-1 * -7a + a * -7a) + 1
11 + -4a = (7a + -7a2) + 1

Reorder the terms:
11 + -4a = 1 + 7a + -7a2

Solving
11 + -4a = 1 + 7a + -7a2

Solving for variable 'a'.

Reorder the terms:
11 + -1 + -4a + -7a + 7a2 = 1 + 7a + -7a2 + -1 + -7a + 7a2

Combine like terms: 11 + -1 = 10
10 + -4a + -7a + 7a2 = 1 + 7a + -7a2 + -1 + -7a + 7a2

Combine like terms: -4a + -7a = -11a
10 + -11a + 7a2 = 1 + 7a + -7a2 + -1 + -7a + 7a2

Reorder the terms:
10 + -11a + 7a2 = 1 + -1 + 7a + -7a + -7a2 + 7a2

Combine like terms: 1 + -1 = 0
10 + -11a + 7a2 = 0 + 7a + -7a + -7a2 + 7a2
10 + -11a + 7a2 = 7a + -7a + -7a2 + 7a2

Combine like terms: 7a + -7a = 0
10 + -11a + 7a2 = 0 + -7a2 + 7a2
10 + -11a + 7a2 = -7a2 + 7a2

Combine like terms: -7a2 + 7a2 = 0
10 + -11a + 7a2 = 0

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

Divide each side by '7'.
1.428571429 + -1.571428571a + a2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + -1.571428571a + -1.428571429 + a2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + -1.571428571a + a2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + -1.571428571a + a2 = 0 + -1.428571429
-1.571428571a + a2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
-1.571428571a + a2 = -1.428571429

The a term is -1.571428571a.  Take half its coefficient (-0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
-1.571428571a + 0.6173469384 + a2 = -1.428571429 + 0.6173469384

Reorder the terms:
0.6173469384 + -1.571428571a + a2 = -1.428571429 + 0.6173469384

Combine like terms: -1.428571429 + 0.6173469384 = -0.8112244906
0.6173469384 + -1.571428571a + a2 = -0.8112244906

Factor a perfect square on the left side:
(a + -0.7857142855)(a + -0.7857142855) = -0.8112244906

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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