x^2+19x+90.25=25

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Solution for x^2+19x+90.25=25 equation: 


Simplifying
x2 + 19x + 90.25 = 25

Reorder the terms:
90.25 + 19x + x2 = 25

Solving
90.25 + 19x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
90.25 + -25 + 19x + x2 = 25 + -25

Combine like terms: 90.25 + -25 = 65.25
65.25 + 19x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
65.25 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-65.25' to each side of the equation.
65.25 + 19x + -65.25 + x2 = 0 + -65.25

Reorder the terms:
65.25 + -65.25 + 19x + x2 = 0 + -65.25

Combine like terms: 65.25 + -65.25 = 0.00
0.00 + 19x + x2 = 0 + -65.25
19x + x2 = 0 + -65.25

Combine like terms: 0 + -65.25 = -65.25
19x + x2 = -65.25

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 = -65.25 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -65.25 + 90.25

Combine like terms: -65.25 + 90.25 = 25
90.25 + 19x + x2 = 25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 9.5) equal to 5 and -5.


Subproblem 1
x + 9.5 = 5

Simplifying
x + 9.5 = 5

Reorder the terms:
9.5 + x = 5

Solving
9.5 + x = 5

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 = 5 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 5 + -9.5
x = 5 + -9.5

Combine like terms: 5 + -9.5 = -4.5
x = -4.5

Simplifying
x = -4.5


Subproblem 2
x + 9.5 = -5

Simplifying
x + 9.5 = -5

Reorder the terms:
9.5 + x = -5

Solving
9.5 + x = -5

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 = -5 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -5 + -9.5
x = -5 + -9.5

Combine like terms: -5 + -9.5 = -14.5
x = -14.5

Simplifying
x = -14.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.5, -14.5}

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