x^2-10*x-18=0

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Solution for x^2-10*x-18=0 equation:


Simplifying
x2 + -10x + -18 = 0

Reorder the terms:
-18 + -10x + x2 = 0

Solving
-18 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -10x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -10x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -10x + x2 = 0 + 18
-10x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-10x + x2 = 18

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 = 18 + 25

Reorder the terms:
25 + -10x + x2 = 18 + 25

Combine like terms: 18 + 25 = 43
25 + -10x + x2 = 43

Factor a perfect square on the left side:
(x + -5)(x + -5) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + -5) equal to 6.557438524 and -6.557438524.

Subproblem 1

x + -5 = 6.557438524 Simplifying x + -5 = 6.557438524 Reorder the terms: -5 + x = 6.557438524 Solving -5 + x = 6.557438524 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 = 6.557438524 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.557438524 + 5 x = 6.557438524 + 5 Combine like terms: 6.557438524 + 5 = 11.557438524 x = 11.557438524 Simplifying x = 11.557438524

Subproblem 2

x + -5 = -6.557438524 Simplifying x + -5 = -6.557438524 Reorder the terms: -5 + x = -6.557438524 Solving -5 + x = -6.557438524 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 = -6.557438524 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.557438524 + 5 x = -6.557438524 + 5 Combine like terms: -6.557438524 + 5 = -1.557438524 x = -1.557438524 Simplifying x = -1.557438524

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.557438524, -1.557438524}

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