-x^2+18x+25=0

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Solution for -x^2+18x+25=0 equation: 


Simplifying
-1x2 + 18x + 25 = 0

Reorder the terms:
25 + 18x + -1x2 = 0

Solving
25 + 18x + -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'.
-25 + -18x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -18x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -18x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -18x + x2 = 0 + 25
-18x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-18x + x2 = 25

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 25 + 81

Reorder the terms:
81 + -18x + x2 = 25 + 81

Combine like terms: 25 + 81 = 106
81 + -18x + x2 = 106

Factor a perfect square on the left side:
(x + -9)(x + -9) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -9) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -9 = 10.295630141

Simplifying
x + -9 = 10.295630141

Reorder the terms:
-9 + x = 10.295630141

Solving
-9 + x = 10.295630141

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + x = 10.295630141 + 9
x = 10.295630141 + 9

Combine like terms: 10.295630141 + 9 = 19.295630141
x = 19.295630141

Simplifying
x = 19.295630141


Subproblem 2
x + -9 = -10.295630141

Simplifying
x + -9 = -10.295630141

Reorder the terms:
-9 + x = -10.295630141

Solving
-9 + x = -10.295630141

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + x = -10.295630141 + 9
x = -10.295630141 + 9

Combine like terms: -10.295630141 + 9 = -1.295630141
x = -1.295630141

Simplifying
x = -1.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.295630141, -1.295630141}

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