x^2+3x-720=0

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Solution for x^2+3x-720=0 equation: 


Simplifying
x2 + 3x + -720 = 0

Reorder the terms:
-720 + 3x + x2 = 0

Solving
-720 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '720' to each side of the equation.
-720 + 3x + 720 + x2 = 0 + 720

Reorder the terms:
-720 + 720 + 3x + x2 = 0 + 720

Combine like terms: -720 + 720 = 0
0 + 3x + x2 = 0 + 720
3x + x2 = 0 + 720

Combine like terms: 0 + 720 = 720
3x + x2 = 720

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 720 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 720 + 2.25

Combine like terms: 720 + 2.25 = 722.25
2.25 + 3x + x2 = 722.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 722.25

Calculate the square root of the right side: 26.874709301

Break this problem into two subproblems by setting 
(x + 1.5) equal to 26.874709301 and -26.874709301.


Subproblem 1
x + 1.5 = 26.874709301

Simplifying
x + 1.5 = 26.874709301

Reorder the terms:
1.5 + x = 26.874709301

Solving
1.5 + x = 26.874709301

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 26.874709301 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 26.874709301 + -1.5
x = 26.874709301 + -1.5

Combine like terms: 26.874709301 + -1.5 = 25.374709301
x = 25.374709301

Simplifying
x = 25.374709301


Subproblem 2
x + 1.5 = -26.874709301

Simplifying
x + 1.5 = -26.874709301

Reorder the terms:
1.5 + x = -26.874709301

Solving
1.5 + x = -26.874709301

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -26.874709301 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -26.874709301 + -1.5
x = -26.874709301 + -1.5

Combine like terms: -26.874709301 + -1.5 = -28.374709301
x = -28.374709301

Simplifying
x = -28.374709301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.374709301, -28.374709301}

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