21000=850x+x^2

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Solution for 21000=850x+x^2 equation:


Simplifying
21000 = 850x + x2

Solving
21000 = 850x + x2

Solving for variable 'x'.

Reorder the terms:
21000 + -850x + -1x2 = 850x + -850x + x2 + -1x2

Combine like terms: 850x + -850x = 0
21000 + -850x + -1x2 = 0 + x2 + -1x2
21000 + -850x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21000 + -850x + -1x2 = 0

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

Divide each side by '-1'.
-21000 + 850x + x2 = 0

Move the constant term to the right:

Add '21000' to each side of the equation.
-21000 + 850x + 21000 + x2 = 0 + 21000

Reorder the terms:
-21000 + 21000 + 850x + x2 = 0 + 21000

Combine like terms: -21000 + 21000 = 0
0 + 850x + x2 = 0 + 21000
850x + x2 = 0 + 21000

Combine like terms: 0 + 21000 = 21000
850x + x2 = 21000

The x term is 850x.  Take half its coefficient (425).
Square it (180625) and add it to both sides.

Add '180625' to each side of the equation.
850x + 180625 + x2 = 21000 + 180625

Reorder the terms:
180625 + 850x + x2 = 21000 + 180625

Combine like terms: 21000 + 180625 = 201625
180625 + 850x + x2 = 201625

Factor a perfect square on the left side:
(x + 425)(x + 425) = 201625

Calculate the square root of the right side: 449.026725263

Break this problem into two subproblems by setting 
(x + 425) equal to 449.026725263 and -449.026725263.

Subproblem 1

x + 425 = 449.026725263 Simplifying x + 425 = 449.026725263 Reorder the terms: 425 + x = 449.026725263 Solving 425 + x = 449.026725263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-425' to each side of the equation. 425 + -425 + x = 449.026725263 + -425 Combine like terms: 425 + -425 = 0 0 + x = 449.026725263 + -425 x = 449.026725263 + -425 Combine like terms: 449.026725263 + -425 = 24.026725263 x = 24.026725263 Simplifying x = 24.026725263

Subproblem 2

x + 425 = -449.026725263 Simplifying x + 425 = -449.026725263 Reorder the terms: 425 + x = -449.026725263 Solving 425 + x = -449.026725263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-425' to each side of the equation. 425 + -425 + x = -449.026725263 + -425 Combine like terms: 425 + -425 = 0 0 + x = -449.026725263 + -425 x = -449.026725263 + -425 Combine like terms: -449.026725263 + -425 = -874.026725263 x = -874.026725263 Simplifying x = -874.026725263

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.026725263, -874.026725263}

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