a^2-14a+49=3

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Solution for a^2-14a+49=3 equation:


Simplifying
a2 + -14a + 49 = 3

Reorder the terms:
49 + -14a + a2 = 3

Solving
49 + -14a + a2 = 3

Solving for variable 'a'.

Reorder the terms:
49 + -3 + -14a + a2 = 3 + -3

Combine like terms: 49 + -3 = 46
46 + -14a + a2 = 3 + -3

Combine like terms: 3 + -3 = 0
46 + -14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -14a + -46 + a2 = 0 + -46

Reorder the terms:
46 + -46 + -14a + a2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -14a + a2 = 0 + -46
-14a + a2 = 0 + -46

Combine like terms: 0 + -46 = -46
-14a + a2 = -46

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = -46 + 49

Reorder the terms:
49 + -14a + a2 = -46 + 49

Combine like terms: -46 + 49 = 3
49 + -14a + a2 = 3

Factor a perfect square on the left side:
(a + -7)(a + -7) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + -7) equal to 1.732050808 and -1.732050808.

Subproblem 1

a + -7 = 1.732050808 Simplifying a + -7 = 1.732050808 Reorder the terms: -7 + a = 1.732050808 Solving -7 + a = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + a = 1.732050808 + 7 a = 1.732050808 + 7 Combine like terms: 1.732050808 + 7 = 8.732050808 a = 8.732050808 Simplifying a = 8.732050808

Subproblem 2

a + -7 = -1.732050808 Simplifying a + -7 = -1.732050808 Reorder the terms: -7 + a = -1.732050808 Solving -7 + a = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + a = -1.732050808 + 7 a = -1.732050808 + 7 Combine like terms: -1.732050808 + 7 = 5.267949192 a = 5.267949192 Simplifying a = 5.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.732050808, 5.267949192}

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