-x^2-64x+16=0

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Solution for -x^2-64x+16=0 equation:


Simplifying
-1x2 + -64x + 16 = 0

Reorder the terms:
16 + -64x + -1x2 = 0

Solving
16 + -64x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + 64x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 64x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 64x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 64x + x2 = 0 + 16
64x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
64x + x2 = 16

The x term is 64x.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64x + 1024 + x2 = 16 + 1024

Reorder the terms:
1024 + 64x + x2 = 16 + 1024

Combine like terms: 16 + 1024 = 1040
1024 + 64x + x2 = 1040

Factor a perfect square on the left side:
(x + 32)(x + 32) = 1040

Calculate the square root of the right side: 32.249030993

Break this problem into two subproblems by setting 
(x + 32) equal to 32.249030993 and -32.249030993.

Subproblem 1

x + 32 = 32.249030993 Simplifying x + 32 = 32.249030993 Reorder the terms: 32 + x = 32.249030993 Solving 32 + x = 32.249030993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 32.249030993 + -32 Combine like terms: 32 + -32 = 0 0 + x = 32.249030993 + -32 x = 32.249030993 + -32 Combine like terms: 32.249030993 + -32 = 0.249030993 x = 0.249030993 Simplifying x = 0.249030993

Subproblem 2

x + 32 = -32.249030993 Simplifying x + 32 = -32.249030993 Reorder the terms: 32 + x = -32.249030993 Solving 32 + x = -32.249030993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -32.249030993 + -32 Combine like terms: 32 + -32 = 0 0 + x = -32.249030993 + -32 x = -32.249030993 + -32 Combine like terms: -32.249030993 + -32 = -64.249030993 x = -64.249030993 Simplifying x = -64.249030993

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.249030993, -64.249030993}

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