1x^2-5x-5000=0

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Solution for 1x^2-5x-5000=0 equation:


Simplifying
1x2 + -5x + -5000 = 0

Reorder the terms:
-5000 + -5x + 1x2 = 0

Solving
-5000 + -5x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + -5x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + -5x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + -5x + x2 = 0 + 5000
-5x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
-5x + x2 = 5000

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 5000 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 5000 + 6.25

Combine like terms: 5000 + 6.25 = 5006.25
6.25 + -5x + x2 = 5006.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5006.25

Calculate the square root of the right side: 70.75485849

Break this problem into two subproblems by setting 
(x + -2.5) equal to 70.75485849 and -70.75485849.

Subproblem 1

x + -2.5 = 70.75485849 Simplifying x + -2.5 = 70.75485849 Reorder the terms: -2.5 + x = 70.75485849 Solving -2.5 + x = 70.75485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 70.75485849 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 70.75485849 + 2.5 x = 70.75485849 + 2.5 Combine like terms: 70.75485849 + 2.5 = 73.25485849 x = 73.25485849 Simplifying x = 73.25485849

Subproblem 2

x + -2.5 = -70.75485849 Simplifying x + -2.5 = -70.75485849 Reorder the terms: -2.5 + x = -70.75485849 Solving -2.5 + x = -70.75485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -70.75485849 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -70.75485849 + 2.5 x = -70.75485849 + 2.5 Combine like terms: -70.75485849 + 2.5 = -68.25485849 x = -68.25485849 Simplifying x = -68.25485849

Solution

The solution to the problem is based on the solutions from the subproblems. x = {73.25485849, -68.25485849}

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