x^2-9x-50=0

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Solution for x^2-9x-50=0 equation:


Simplifying
x2 + -9x + -50 = 0

Reorder the terms:
-50 + -9x + x2 = 0

Solving
-50 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -9x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -9x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -9x + x2 = 0 + 50
-9x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-9x + x2 = 50

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 50 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 50 + 20.25

Combine like terms: 50 + 20.25 = 70.25
20.25 + -9x + x2 = 70.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + -4.5) equal to 8.381527307 and -8.381527307.

Subproblem 1

x + -4.5 = 8.381527307 Simplifying x + -4.5 = 8.381527307 Reorder the terms: -4.5 + x = 8.381527307 Solving -4.5 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 8.381527307 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 8.381527307 + 4.5 x = 8.381527307 + 4.5 Combine like terms: 8.381527307 + 4.5 = 12.881527307 x = 12.881527307 Simplifying x = 12.881527307

Subproblem 2

x + -4.5 = -8.381527307 Simplifying x + -4.5 = -8.381527307 Reorder the terms: -4.5 + x = -8.381527307 Solving -4.5 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -8.381527307 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -8.381527307 + 4.5 x = -8.381527307 + 4.5 Combine like terms: -8.381527307 + 4.5 = -3.881527307 x = -3.881527307 Simplifying x = -3.881527307

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.881527307, -3.881527307}

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