x^2+19x-207=0

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Solution for x^2+19x-207=0 equation: 


Simplifying
x2 + 19x + -207 = 0

Reorder the terms:
-207 + 19x + x2 = 0

Solving
-207 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '207' to each side of the equation.
-207 + 19x + 207 + x2 = 0 + 207

Reorder the terms:
-207 + 207 + 19x + x2 = 0 + 207

Combine like terms: -207 + 207 = 0
0 + 19x + x2 = 0 + 207
19x + x2 = 0 + 207

Combine like terms: 0 + 207 = 207
19x + x2 = 207

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 = 207 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 207 + 90.25

Combine like terms: 207 + 90.25 = 297.25
90.25 + 19x + x2 = 297.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 297.25

Calculate the square root of the right side: 17.24093965

Break this problem into two subproblems by setting 
(x + 9.5) equal to 17.24093965 and -17.24093965.


Subproblem 1
x + 9.5 = 17.24093965

Simplifying
x + 9.5 = 17.24093965

Reorder the terms:
9.5 + x = 17.24093965

Solving
9.5 + x = 17.24093965

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 = 17.24093965 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 17.24093965 + -9.5
x = 17.24093965 + -9.5

Combine like terms: 17.24093965 + -9.5 = 7.74093965
x = 7.74093965

Simplifying
x = 7.74093965


Subproblem 2
x + 9.5 = -17.24093965

Simplifying
x + 9.5 = -17.24093965

Reorder the terms:
9.5 + x = -17.24093965

Solving
9.5 + x = -17.24093965

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 = -17.24093965 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -17.24093965 + -9.5
x = -17.24093965 + -9.5

Combine like terms: -17.24093965 + -9.5 = -26.74093965
x = -26.74093965

Simplifying
x = -26.74093965


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.74093965, -26.74093965}

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