-x^2+15x-18=0

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Solution for -x^2+15x-18=0 equation: 


Simplifying
-1x2 + 15x + -18 = 0

Reorder the terms:
-18 + 15x + -1x2 = 0

Solving
-18 + 15x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
18 + -15x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -15x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -15x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -15x + x2 = 0 + -18
-15x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-15x + x2 = -18

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -18 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -18 + 56.25

Combine like terms: -18 + 56.25 = 38.25
56.25 + -15x + x2 = 38.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + -7.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + -7.5 = 6.184658438

Simplifying
x + -7.5 = 6.184658438

Reorder the terms:
-7.5 + x = 6.184658438

Solving
-7.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 6.184658438 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 6.184658438 + 7.5
x = 6.184658438 + 7.5

Combine like terms: 6.184658438 + 7.5 = 13.684658438
x = 13.684658438

Simplifying
x = 13.684658438


Subproblem 2
x + -7.5 = -6.184658438

Simplifying
x + -7.5 = -6.184658438

Reorder the terms:
-7.5 + x = -6.184658438

Solving
-7.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -6.184658438 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -6.184658438 + 7.5
x = -6.184658438 + 7.5

Combine like terms: -6.184658438 + 7.5 = 1.315341562
x = 1.315341562

Simplifying
x = 1.315341562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.684658438, 1.315341562}

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