-X^2+13X+15=0

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Solution for -X^2+13X+15=0 equation: 


Simplifying
-1X2 + 13X + 15 = 0

Reorder the terms:
15 + 13X + -1X2 = 0

Solving
15 + 13X + -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'.
-15 + -13X + X2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -13X + 15 + X2 = 0 + 15

Reorder the terms:
-15 + 15 + -13X + X2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -13X + X2 = 0 + 15
-13X + X2 = 0 + 15

Combine like terms: 0 + 15 = 15
-13X + X2 = 15

The X term is -13X.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13X + 42.25 + X2 = 15 + 42.25

Reorder the terms:
42.25 + -13X + X2 = 15 + 42.25

Combine like terms: 15 + 42.25 = 57.25
42.25 + -13X + X2 = 57.25

Factor a perfect square on the left side:
(X + -6.5)(X + -6.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(X + -6.5) equal to 7.566372975 and -7.566372975.


Subproblem 1
X + -6.5 = 7.566372975

Simplifying
X + -6.5 = 7.566372975

Reorder the terms:
-6.5 + X = 7.566372975

Solving
-6.5 + X = 7.566372975

Solving for variable 'X'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + X = 7.566372975 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + X = 7.566372975 + 6.5
X = 7.566372975 + 6.5

Combine like terms: 7.566372975 + 6.5 = 14.066372975
X = 14.066372975

Simplifying
X = 14.066372975


Subproblem 2
X + -6.5 = -7.566372975

Simplifying
X + -6.5 = -7.566372975

Reorder the terms:
-6.5 + X = -7.566372975

Solving
-6.5 + X = -7.566372975

Solving for variable 'X'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + X = -7.566372975 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + X = -7.566372975 + 6.5
X = -7.566372975 + 6.5

Combine like terms: -7.566372975 + 6.5 = -1.066372975
X = -1.066372975

Simplifying
X = -1.066372975


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {14.066372975, -1.066372975}

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