a^2-14a-21=0

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Solution for a^2-14a-21=0 equation: 


Simplifying
a2 + -14a + -21 = 0

Reorder the terms:
-21 + -14a + a2 = 0

Solving
-21 + -14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -14a + 21 + a2 = 0 + 21

Reorder the terms:
-21 + 21 + -14a + a2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -14a + a2 = 0 + 21
-14a + a2 = 0 + 21

Combine like terms: 0 + 21 = 21
-14a + a2 = 21

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 = 21 + 49

Reorder the terms:
49 + -14a + a2 = 21 + 49

Combine like terms: 21 + 49 = 70
49 + -14a + a2 = 70

Factor a perfect square on the left side:
(a + -7)(a + -7) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(a + -7) equal to 8.366600265 and -8.366600265.


Subproblem 1
a + -7 = 8.366600265

Simplifying
a + -7 = 8.366600265

Reorder the terms:
-7 + a = 8.366600265

Solving
-7 + a = 8.366600265

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 = 8.366600265 + 7

Combine like terms: -7 + 7 = 0
0 + a = 8.366600265 + 7
a = 8.366600265 + 7

Combine like terms: 8.366600265 + 7 = 15.366600265
a = 15.366600265

Simplifying
a = 15.366600265


Subproblem 2
a + -7 = -8.366600265

Simplifying
a + -7 = -8.366600265

Reorder the terms:
-7 + a = -8.366600265

Solving
-7 + a = -8.366600265

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 = -8.366600265 + 7

Combine like terms: -7 + 7 = 0
0 + a = -8.366600265 + 7
a = -8.366600265 + 7

Combine like terms: -8.366600265 + 7 = -1.366600265
a = -1.366600265

Simplifying
a = -1.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {15.366600265, -1.366600265}

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