x^2-20x-18=7

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Solution for x^2-20x-18=7 equation: 


Simplifying
x2 + -20x + -18 = 7

Reorder the terms:
-18 + -20x + x2 = 7

Solving
-18 + -20x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-18 + -7 + -20x + x2 = 7 + -7

Combine like terms: -18 + -7 = -25
-25 + -20x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-25 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -20x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -20x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -20x + x2 = 0 + 25
-20x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-20x + x2 = 25

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 25 + 100

Reorder the terms:
100 + -20x + x2 = 25 + 100

Combine like terms: 25 + 100 = 125
100 + -20x + x2 = 125

Factor a perfect square on the left side:
(x + -10)(x + -10) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + -10) equal to 11.180339887 and -11.180339887.


Subproblem 1
x + -10 = 11.180339887

Simplifying
x + -10 = 11.180339887

Reorder the terms:
-10 + x = 11.180339887

Solving
-10 + x = 11.180339887

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = 11.180339887 + 10

Combine like terms: -10 + 10 = 0
0 + x = 11.180339887 + 10
x = 11.180339887 + 10

Combine like terms: 11.180339887 + 10 = 21.180339887
x = 21.180339887

Simplifying
x = 21.180339887


Subproblem 2
x + -10 = -11.180339887

Simplifying
x + -10 = -11.180339887

Reorder the terms:
-10 + x = -11.180339887

Solving
-10 + x = -11.180339887

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = -11.180339887 + 10

Combine like terms: -10 + 10 = 0
0 + x = -11.180339887 + 10
x = -11.180339887 + 10

Combine like terms: -11.180339887 + 10 = -1.180339887
x = -1.180339887

Simplifying
x = -1.180339887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.180339887, -1.180339887}

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