7(a+1)-2a=5+4a(a-1)

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Solution for 7(a+1)-2a=5+4a(a-1) equation:


Simplifying
7(a + 1) + -2a = 5 + 4a(a + -1)

Reorder the terms:
7(1 + a) + -2a = 5 + 4a(a + -1)
(1 * 7 + a * 7) + -2a = 5 + 4a(a + -1)
(7 + 7a) + -2a = 5 + 4a(a + -1)

Combine like terms: 7a + -2a = 5a
7 + 5a = 5 + 4a(a + -1)

Reorder the terms:
7 + 5a = 5 + 4a(-1 + a)
7 + 5a = 5 + (-1 * 4a + a * 4a)
7 + 5a = 5 + (-4a + 4a2)

Solving
7 + 5a = 5 + -4a + 4a2

Solving for variable 'a'.

Reorder the terms:
7 + -5 + 5a + 4a + -4a2 = 5 + -4a + 4a2 + -5 + 4a + -4a2

Combine like terms: 7 + -5 = 2
2 + 5a + 4a + -4a2 = 5 + -4a + 4a2 + -5 + 4a + -4a2

Combine like terms: 5a + 4a = 9a
2 + 9a + -4a2 = 5 + -4a + 4a2 + -5 + 4a + -4a2

Reorder the terms:
2 + 9a + -4a2 = 5 + -5 + -4a + 4a + 4a2 + -4a2

Combine like terms: 5 + -5 = 0
2 + 9a + -4a2 = 0 + -4a + 4a + 4a2 + -4a2
2 + 9a + -4a2 = -4a + 4a + 4a2 + -4a2

Combine like terms: -4a + 4a = 0
2 + 9a + -4a2 = 0 + 4a2 + -4a2
2 + 9a + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
2 + 9a + -4a2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.5 + -2.25a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2.25a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2.25a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2.25a + a2 = 0 + 0.5
-2.25a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2.25a + a2 = 0.5

The a term is -2.25a.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25a + 1.265625 + a2 = 0.5 + 1.265625

Reorder the terms:
1.265625 + -2.25a + a2 = 0.5 + 1.265625

Combine like terms: 0.5 + 1.265625 = 1.765625
1.265625 + -2.25a + a2 = 1.765625

Factor a perfect square on the left side:
(a + -1.125)(a + -1.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(a + -1.125) equal to 1.328768227 and -1.328768227.

Subproblem 1

a + -1.125 = 1.328768227 Simplifying a + -1.125 = 1.328768227 Reorder the terms: -1.125 + a = 1.328768227 Solving -1.125 + a = 1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + a = 1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + a = 1.328768227 + 1.125 a = 1.328768227 + 1.125 Combine like terms: 1.328768227 + 1.125 = 2.453768227 a = 2.453768227 Simplifying a = 2.453768227

Subproblem 2

a + -1.125 = -1.328768227 Simplifying a + -1.125 = -1.328768227 Reorder the terms: -1.125 + a = -1.328768227 Solving -1.125 + a = -1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + a = -1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + a = -1.328768227 + 1.125 a = -1.328768227 + 1.125 Combine like terms: -1.328768227 + 1.125 = -0.203768227 a = -0.203768227 Simplifying a = -0.203768227

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.453768227, -0.203768227}

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