x+x^2=5000

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Solution for x+x^2=5000 equation:


Simplifying
x + x2 = 5000

Solving
x + x2 = 5000

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 5000 + 0.25

Reorder the terms:
0.25 + x + x2 = 5000 + 0.25

Combine like terms: 5000 + 0.25 = 5000.25
0.25 + x + x2 = 5000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5000.25

Calculate the square root of the right side: 70.712445864

Break this problem into two subproblems by setting 
(x + 0.5) equal to 70.712445864 and -70.712445864.

Subproblem 1

x + 0.5 = 70.712445864 Simplifying x + 0.5 = 70.712445864 Reorder the terms: 0.5 + x = 70.712445864 Solving 0.5 + x = 70.712445864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 70.712445864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 70.712445864 + -0.5 x = 70.712445864 + -0.5 Combine like terms: 70.712445864 + -0.5 = 70.212445864 x = 70.212445864 Simplifying x = 70.212445864

Subproblem 2

x + 0.5 = -70.712445864 Simplifying x + 0.5 = -70.712445864 Reorder the terms: 0.5 + x = -70.712445864 Solving 0.5 + x = -70.712445864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -70.712445864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -70.712445864 + -0.5 x = -70.712445864 + -0.5 Combine like terms: -70.712445864 + -0.5 = -71.212445864 x = -71.212445864 Simplifying x = -71.212445864

Solution

The solution to the problem is based on the solutions from the subproblems. x = {70.212445864, -71.212445864}

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