x^2-19x-18=0

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Solution for x^2-19x-18=0 equation:


Simplifying
x2 + -19x + -18 = 0

Reorder the terms:
-18 + -19x + x2 = 0

Solving
-18 + -19x + 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 + -19x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -19x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -19x + x2 = 0 + 18
-19x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-19x + x2 = 18

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 18 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 18 + 90.25

Combine like terms: 18 + 90.25 = 108.25
90.25 + -19x + x2 = 108.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 108.25

Calculate the square root of the right side: 10.404326023

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10.404326023 and -10.404326023.

Subproblem 1

x + -9.5 = 10.404326023 Simplifying x + -9.5 = 10.404326023 Reorder the terms: -9.5 + x = 10.404326023 Solving -9.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.404326023 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.404326023 + 9.5 x = 10.404326023 + 9.5 Combine like terms: 10.404326023 + 9.5 = 19.904326023 x = 19.904326023 Simplifying x = 19.904326023

Subproblem 2

x + -9.5 = -10.404326023 Simplifying x + -9.5 = -10.404326023 Reorder the terms: -9.5 + x = -10.404326023 Solving -9.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.404326023 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.404326023 + 9.5 x = -10.404326023 + 9.5 Combine like terms: -10.404326023 + 9.5 = -0.904326023 x = -0.904326023 Simplifying x = -0.904326023

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.904326023, -0.904326023}

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