13-(4a-1)2=(4a+7)(7-4a)-37

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Solution for 13-(4a-1)2=(4a+7)(7-4a)-37 equation: 


Simplifying
13 + -1(4a + -1) * 2 = (4a + 7)(7 + -4a) + -37

Reorder the terms:
13 + -1(-1 + 4a) * 2 = (4a + 7)(7 + -4a) + -37

Reorder the terms for easier multiplication:
13 + -1 * 2(-1 + 4a) = (4a + 7)(7 + -4a) + -37

Multiply -1 * 2
13 + -2(-1 + 4a) = (4a + 7)(7 + -4a) + -37
13 + (-1 * -2 + 4a * -2) = (4a + 7)(7 + -4a) + -37
13 + (2 + -8a) = (4a + 7)(7 + -4a) + -37

Combine like terms: 13 + 2 = 15
15 + -8a = (4a + 7)(7 + -4a) + -37

Reorder the terms:
15 + -8a = (7 + 4a)(7 + -4a) + -37

Multiply (7 + 4a) * (7 + -4a)
15 + -8a = (7(7 + -4a) + 4a * (7 + -4a)) + -37
15 + -8a = ((7 * 7 + -4a * 7) + 4a * (7 + -4a)) + -37
15 + -8a = ((49 + -28a) + 4a * (7 + -4a)) + -37
15 + -8a = (49 + -28a + (7 * 4a + -4a * 4a)) + -37
15 + -8a = (49 + -28a + (28a + -16a2)) + -37

Combine like terms: -28a + 28a = 0
15 + -8a = (49 + 0 + -16a2) + -37
15 + -8a = (49 + -16a2) + -37

Reorder the terms:
15 + -8a = 49 + -37 + -16a2

Combine like terms: 49 + -37 = 12
15 + -8a = 12 + -16a2

Solving
15 + -8a = 12 + -16a2

Solving for variable 'a'.

Reorder the terms:
15 + -12 + -8a + 16a2 = 12 + -16a2 + -12 + 16a2

Combine like terms: 15 + -12 = 3
3 + -8a + 16a2 = 12 + -16a2 + -12 + 16a2

Reorder the terms:
3 + -8a + 16a2 = 12 + -12 + -16a2 + 16a2

Combine like terms: 12 + -12 = 0
3 + -8a + 16a2 = 0 + -16a2 + 16a2
3 + -8a + 16a2 = -16a2 + 16a2

Combine like terms: -16a2 + 16a2 = 0
3 + -8a + 16a2 = 0

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

Divide each side by '16'.
0.1875 + -0.5a + a2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + -0.5a + -0.1875 + a2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + -0.5a + a2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + -0.5a + a2 = 0 + -0.1875
-0.5a + a2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
-0.5a + a2 = -0.1875

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = -0.1875 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = -0.1875 + 0.0625

Combine like terms: -0.1875 + 0.0625 = -0.125
0.0625 + -0.5a + a2 = -0.125

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = -0.125

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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