a^2-16a-27=0

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Solution for a^2-16a-27=0 equation:


Simplifying
a2 + -16a + -27 = 0

Reorder the terms:
-27 + -16a + a2 = 0

Solving
-27 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -16a + 27 + a2 = 0 + 27

Reorder the terms:
-27 + 27 + -16a + a2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -16a + a2 = 0 + 27
-16a + a2 = 0 + 27

Combine like terms: 0 + 27 = 27
-16a + a2 = 27

The a term is -16a.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16a + 64 + a2 = 27 + 64

Reorder the terms:
64 + -16a + a2 = 27 + 64

Combine like terms: 27 + 64 = 91
64 + -16a + a2 = 91

Factor a perfect square on the left side:
(a + -8)(a + -8) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(a + -8) equal to 9.539392014 and -9.539392014.

Subproblem 1

a + -8 = 9.539392014 Simplifying a + -8 = 9.539392014 Reorder the terms: -8 + a = 9.539392014 Solving -8 + a = 9.539392014 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = 9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + a = 9.539392014 + 8 a = 9.539392014 + 8 Combine like terms: 9.539392014 + 8 = 17.539392014 a = 17.539392014 Simplifying a = 17.539392014

Subproblem 2

a + -8 = -9.539392014 Simplifying a + -8 = -9.539392014 Reorder the terms: -8 + a = -9.539392014 Solving -8 + a = -9.539392014 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = -9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + a = -9.539392014 + 8 a = -9.539392014 + 8 Combine like terms: -9.539392014 + 8 = -1.539392014 a = -1.539392014 Simplifying a = -1.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. a = {17.539392014, -1.539392014}

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