a^2-16a-63=0

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Solution for a^2-16a-63=0 equation:


Simplifying
a2 + -16a + -63 = 0

Reorder the terms:
-63 + -16a + a2 = 0

Solving
-63 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + -16a + 63 + a2 = 0 + 63

Reorder the terms:
-63 + 63 + -16a + a2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -16a + a2 = 0 + 63
-16a + a2 = 0 + 63

Combine like terms: 0 + 63 = 63
-16a + a2 = 63

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 = 63 + 64

Reorder the terms:
64 + -16a + a2 = 63 + 64

Combine like terms: 63 + 64 = 127
64 + -16a + a2 = 127

Factor a perfect square on the left side:
(a + -8)(a + -8) = 127

Calculate the square root of the right side: 11.26942767

Break this problem into two subproblems by setting 
(a + -8) equal to 11.26942767 and -11.26942767.

Subproblem 1

a + -8 = 11.26942767 Simplifying a + -8 = 11.26942767 Reorder the terms: -8 + a = 11.26942767 Solving -8 + a = 11.26942767 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 = 11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + a = 11.26942767 + 8 a = 11.26942767 + 8 Combine like terms: 11.26942767 + 8 = 19.26942767 a = 19.26942767 Simplifying a = 19.26942767

Subproblem 2

a + -8 = -11.26942767 Simplifying a + -8 = -11.26942767 Reorder the terms: -8 + a = -11.26942767 Solving -8 + a = -11.26942767 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 = -11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + a = -11.26942767 + 8 a = -11.26942767 + 8 Combine like terms: -11.26942767 + 8 = -3.26942767 a = -3.26942767 Simplifying a = -3.26942767

Solution

The solution to the problem is based on the solutions from the subproblems. a = {19.26942767, -3.26942767}

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