a^2-2a-49=3

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Solution for a^2-2a-49=3 equation:


Simplifying
a2 + -2a + -49 = 3

Reorder the terms:
-49 + -2a + a2 = 3

Solving
-49 + -2a + a2 = 3

Solving for variable 'a'.

Reorder the terms:
-49 + -3 + -2a + a2 = 3 + -3

Combine like terms: -49 + -3 = -52
-52 + -2a + a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-52 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -2a + 52 + a2 = 0 + 52

Reorder the terms:
-52 + 52 + -2a + a2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -2a + a2 = 0 + 52
-2a + a2 = 0 + 52

Combine like terms: 0 + 52 = 52
-2a + a2 = 52

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 52 + 1

Reorder the terms:
1 + -2a + a2 = 52 + 1

Combine like terms: 52 + 1 = 53
1 + -2a + a2 = 53

Factor a perfect square on the left side:
(a + -1)(a + -1) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(a + -1) equal to 7.280109889 and -7.280109889.

Subproblem 1

a + -1 = 7.280109889 Simplifying a + -1 = 7.280109889 Reorder the terms: -1 + a = 7.280109889 Solving -1 + a = 7.280109889 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + a = 7.280109889 + 1 a = 7.280109889 + 1 Combine like terms: 7.280109889 + 1 = 8.280109889 a = 8.280109889 Simplifying a = 8.280109889

Subproblem 2

a + -1 = -7.280109889 Simplifying a + -1 = -7.280109889 Reorder the terms: -1 + a = -7.280109889 Solving -1 + a = -7.280109889 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + a = -7.280109889 + 1 a = -7.280109889 + 1 Combine like terms: -7.280109889 + 1 = -6.280109889 a = -6.280109889 Simplifying a = -6.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.280109889, -6.280109889}

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