x^2-18x-50=0

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Solution for x^2-18x-50=0 equation:


Simplifying
x2 + -18x + -50 = 0

Reorder the terms:
-50 + -18x + x2 = 0

Solving
-50 + -18x + 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 + -18x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -18x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -18x + x2 = 0 + 50
-18x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-18x + x2 = 50

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 50 + 81

Reorder the terms:
81 + -18x + x2 = 50 + 81

Combine like terms: 50 + 81 = 131
81 + -18x + x2 = 131

Factor a perfect square on the left side:
(x + -9)(x + -9) = 131

Calculate the square root of the right side: 11.445523142

Break this problem into two subproblems by setting 
(x + -9) equal to 11.445523142 and -11.445523142.

Subproblem 1

x + -9 = 11.445523142 Simplifying x + -9 = 11.445523142 Reorder the terms: -9 + x = 11.445523142 Solving -9 + x = 11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.445523142 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.445523142 + 9 x = 11.445523142 + 9 Combine like terms: 11.445523142 + 9 = 20.445523142 x = 20.445523142 Simplifying x = 20.445523142

Subproblem 2

x + -9 = -11.445523142 Simplifying x + -9 = -11.445523142 Reorder the terms: -9 + x = -11.445523142 Solving -9 + x = -11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.445523142 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.445523142 + 9 x = -11.445523142 + 9 Combine like terms: -11.445523142 + 9 = -2.445523142 x = -2.445523142 Simplifying x = -2.445523142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.445523142, -2.445523142}

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