x^2-10x-80=0

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Solution for x^2-10x-80=0 equation:


Simplifying
x2 + -10x + -80 = 0

Reorder the terms:
-80 + -10x + x2 = 0

Solving
-80 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -10x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -10x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -10x + x2 = 0 + 80
-10x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-10x + x2 = 80

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 80 + 25

Reorder the terms:
25 + -10x + x2 = 80 + 25

Combine like terms: 80 + 25 = 105
25 + -10x + x2 = 105

Factor a perfect square on the left side:
(x + -5)(x + -5) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(x + -5) equal to 10.246950766 and -10.246950766.

Subproblem 1

x + -5 = 10.246950766 Simplifying x + -5 = 10.246950766 Reorder the terms: -5 + x = 10.246950766 Solving -5 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.246950766 + 5 x = 10.246950766 + 5 Combine like terms: 10.246950766 + 5 = 15.246950766 x = 15.246950766 Simplifying x = 15.246950766

Subproblem 2

x + -5 = -10.246950766 Simplifying x + -5 = -10.246950766 Reorder the terms: -5 + x = -10.246950766 Solving -5 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.246950766 + 5 x = -10.246950766 + 5 Combine like terms: -10.246950766 + 5 = -5.246950766 x = -5.246950766 Simplifying x = -5.246950766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.246950766, -5.246950766}

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