10000=x^2+12700x

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Solution for 10000=x^2+12700x equation:


Simplifying
10000 = x2 + 12700x

Reorder the terms:
10000 = 12700x + x2

Solving
10000 = 12700x + x2

Solving for variable 'x'.

Reorder the terms:
10000 + -12700x + -1x2 = 12700x + -12700x + x2 + -1x2

Combine like terms: 12700x + -12700x = 0
10000 + -12700x + -1x2 = 0 + x2 + -1x2
10000 + -12700x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10000 + -12700x + -1x2 = 0

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

Divide each side by '-1'.
-10000 + 12700x + x2 = 0

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + 12700x + 10000 + x2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + 12700x + x2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + 12700x + x2 = 0 + 10000
12700x + x2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
12700x + x2 = 10000

The x term is 12700x.  Take half its coefficient (6350).
Square it (40322500) and add it to both sides.

Add '40322500' to each side of the equation.
12700x + 40322500 + x2 = 10000 + 40322500

Reorder the terms:
40322500 + 12700x + x2 = 10000 + 40322500

Combine like terms: 10000 + 40322500 = 40332500
40322500 + 12700x + x2 = 40332500

Factor a perfect square on the left side:
(x + 6350)(x + 6350) = 40332500

Calculate the square root of the right side: 6350.787352762

Break this problem into two subproblems by setting 
(x + 6350) equal to 6350.787352762 and -6350.787352762.

Subproblem 1

x + 6350 = 6350.787352762 Simplifying x + 6350 = 6350.787352762 Reorder the terms: 6350 + x = 6350.787352762 Solving 6350 + x = 6350.787352762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6350' to each side of the equation. 6350 + -6350 + x = 6350.787352762 + -6350 Combine like terms: 6350 + -6350 = 0 0 + x = 6350.787352762 + -6350 x = 6350.787352762 + -6350 Combine like terms: 6350.787352762 + -6350 = 0.787352762 x = 0.787352762 Simplifying x = 0.787352762

Subproblem 2

x + 6350 = -6350.787352762 Simplifying x + 6350 = -6350.787352762 Reorder the terms: 6350 + x = -6350.787352762 Solving 6350 + x = -6350.787352762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6350' to each side of the equation. 6350 + -6350 + x = -6350.787352762 + -6350 Combine like terms: 6350 + -6350 = 0 0 + x = -6350.787352762 + -6350 x = -6350.787352762 + -6350 Combine like terms: -6350.787352762 + -6350 = -12700.787352762 x = -12700.787352762 Simplifying x = -12700.787352762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.787352762, -12700.787352762}

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