a^2+4a-91=7

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Solution for a^2+4a-91=7 equation:


Simplifying
a2 + 4a + -91 = 7

Reorder the terms:
-91 + 4a + a2 = 7

Solving
-91 + 4a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
-91 + -7 + 4a + a2 = 7 + -7

Combine like terms: -91 + -7 = -98
-98 + 4a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-98 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + 4a + 98 + a2 = 0 + 98

Reorder the terms:
-98 + 98 + 4a + a2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 4a + a2 = 0 + 98
4a + a2 = 0 + 98

Combine like terms: 0 + 98 = 98
4a + a2 = 98

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 98 + 4

Reorder the terms:
4 + 4a + a2 = 98 + 4

Combine like terms: 98 + 4 = 102
4 + 4a + a2 = 102

Factor a perfect square on the left side:
(a + 2)(a + 2) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(a + 2) equal to 10.099504938 and -10.099504938.

Subproblem 1

a + 2 = 10.099504938 Simplifying a + 2 = 10.099504938 Reorder the terms: 2 + a = 10.099504938 Solving 2 + a = 10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 10.099504938 + -2 Combine like terms: 2 + -2 = 0 0 + a = 10.099504938 + -2 a = 10.099504938 + -2 Combine like terms: 10.099504938 + -2 = 8.099504938 a = 8.099504938 Simplifying a = 8.099504938

Subproblem 2

a + 2 = -10.099504938 Simplifying a + 2 = -10.099504938 Reorder the terms: 2 + a = -10.099504938 Solving 2 + a = -10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -10.099504938 + -2 Combine like terms: 2 + -2 = 0 0 + a = -10.099504938 + -2 a = -10.099504938 + -2 Combine like terms: -10.099504938 + -2 = -12.099504938 a = -12.099504938 Simplifying a = -12.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.099504938, -12.099504938}

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