x^2+1x=18

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Solution for x^2+1x=18 equation:


Simplifying
x2 + 1x = 18

Reorder the terms:
1x + x2 = 18

Solving
1x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 1x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 1x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 1x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 1x + x2 = 0 + 18
1x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
1x + x2 = 18

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 18 + 0.25

Reorder the terms:
0.25 + x + x2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + x + x2 = 18.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 0.5 = 4.272001873 Simplifying x + 0.5 = 4.272001873 Reorder the terms: 0.5 + x = 4.272001873 Solving 0.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.272001873 + -0.5 x = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 x = 3.772001873 Simplifying x = 3.772001873

Subproblem 2

x + 0.5 = -4.272001873 Simplifying x + 0.5 = -4.272001873 Reorder the terms: 0.5 + x = -4.272001873 Solving 0.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.272001873 + -0.5 x = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 x = -4.772001873 Simplifying x = -4.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.772001873, -4.772001873}

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