-0.25x^2-40x-1000=0

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Solution for -0.25x^2-40x-1000=0 equation:


Simplifying
-0.25x2 + -40x + -1000 = 0

Reorder the terms:
-1000 + -40x + -0.25x2 = 0

Solving
-1000 + -40x + -0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
4000 + 160x + x2 = 0

Move the constant term to the right:

Add '-4000' to each side of the equation.
4000 + 160x + -4000 + x2 = 0 + -4000

Reorder the terms:
4000 + -4000 + 160x + x2 = 0 + -4000

Combine like terms: 4000 + -4000 = 0
0 + 160x + x2 = 0 + -4000
160x + x2 = 0 + -4000

Combine like terms: 0 + -4000 = -4000
160x + x2 = -4000

The x term is 160x.  Take half its coefficient (80).
Square it (6400) and add it to both sides.

Add '6400' to each side of the equation.
160x + 6400 + x2 = -4000 + 6400

Reorder the terms:
6400 + 160x + x2 = -4000 + 6400

Combine like terms: -4000 + 6400 = 2400
6400 + 160x + x2 = 2400

Factor a perfect square on the left side:
(x + 80)(x + 80) = 2400

Calculate the square root of the right side: 48.989794856

Break this problem into two subproblems by setting 
(x + 80) equal to 48.989794856 and -48.989794856.

Subproblem 1

x + 80 = 48.989794856 Simplifying x + 80 = 48.989794856 Reorder the terms: 80 + x = 48.989794856 Solving 80 + x = 48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 48.989794856 + -80 Combine like terms: 80 + -80 = 0 0 + x = 48.989794856 + -80 x = 48.989794856 + -80 Combine like terms: 48.989794856 + -80 = -31.010205144 x = -31.010205144 Simplifying x = -31.010205144

Subproblem 2

x + 80 = -48.989794856 Simplifying x + 80 = -48.989794856 Reorder the terms: 80 + x = -48.989794856 Solving 80 + x = -48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -48.989794856 + -80 Combine like terms: 80 + -80 = 0 0 + x = -48.989794856 + -80 x = -48.989794856 + -80 Combine like terms: -48.989794856 + -80 = -128.989794856 x = -128.989794856 Simplifying x = -128.989794856

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-31.010205144, -128.989794856}

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