-x*x-4x+640=0

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Solution for -x*x-4x+640=0 equation:


Simplifying
-1x * x + -4x + 640 = 0

Multiply x * x
-1x2 + -4x + 640 = 0

Reorder the terms:
640 + -4x + -1x2 = 0

Solving
640 + -4x + -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'.
-640 + 4x + x2 = 0

Move the constant term to the right:

Add '640' to each side of the equation.
-640 + 4x + 640 + x2 = 0 + 640

Reorder the terms:
-640 + 640 + 4x + x2 = 0 + 640

Combine like terms: -640 + 640 = 0
0 + 4x + x2 = 0 + 640
4x + x2 = 0 + 640

Combine like terms: 0 + 640 = 640
4x + x2 = 640

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 640 + 4

Reorder the terms:
4 + 4x + x2 = 640 + 4

Combine like terms: 640 + 4 = 644
4 + 4x + x2 = 644

Factor a perfect square on the left side:
(x + 2)(x + 2) = 644

Calculate the square root of the right side: 25.377155081

Break this problem into two subproblems by setting 
(x + 2) equal to 25.377155081 and -25.377155081.

Subproblem 1

x + 2 = 25.377155081 Simplifying x + 2 = 25.377155081 Reorder the terms: 2 + x = 25.377155081 Solving 2 + x = 25.377155081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 25.377155081 + -2 Combine like terms: 2 + -2 = 0 0 + x = 25.377155081 + -2 x = 25.377155081 + -2 Combine like terms: 25.377155081 + -2 = 23.377155081 x = 23.377155081 Simplifying x = 23.377155081

Subproblem 2

x + 2 = -25.377155081 Simplifying x + 2 = -25.377155081 Reorder the terms: 2 + x = -25.377155081 Solving 2 + x = -25.377155081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -25.377155081 + -2 Combine like terms: 2 + -2 = 0 0 + x = -25.377155081 + -2 x = -25.377155081 + -2 Combine like terms: -25.377155081 + -2 = -27.377155081 x = -27.377155081 Simplifying x = -27.377155081

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.377155081, -27.377155081}

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