x^2-15x-10000=0

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Solution for x^2-15x-10000=0 equation:


Simplifying
x2 + -15x + -10000 = 0

Reorder the terms:
-10000 + -15x + x2 = 0

Solving
-10000 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + -15x + 10000 + x2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + -15x + x2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + -15x + x2 = 0 + 10000
-15x + x2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
-15x + x2 = 10000

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 10000 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 10000 + 56.25

Combine like terms: 10000 + 56.25 = 10056.25
56.25 + -15x + x2 = 10056.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 10056.25

Calculate the square root of the right side: 100.280855601

Break this problem into two subproblems by setting 
(x + -7.5) equal to 100.280855601 and -100.280855601.

Subproblem 1

x + -7.5 = 100.280855601 Simplifying x + -7.5 = 100.280855601 Reorder the terms: -7.5 + x = 100.280855601 Solving -7.5 + x = 100.280855601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 100.280855601 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 100.280855601 + 7.5 x = 100.280855601 + 7.5 Combine like terms: 100.280855601 + 7.5 = 107.780855601 x = 107.780855601 Simplifying x = 107.780855601

Subproblem 2

x + -7.5 = -100.280855601 Simplifying x + -7.5 = -100.280855601 Reorder the terms: -7.5 + x = -100.280855601 Solving -7.5 + x = -100.280855601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -100.280855601 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -100.280855601 + 7.5 x = -100.280855601 + 7.5 Combine like terms: -100.280855601 + 7.5 = -92.780855601 x = -92.780855601 Simplifying x = -92.780855601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {107.780855601, -92.780855601}

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