x^2+2.5x-9=

Solution for x^2+2.5x-9= equation:

Simplifying
x2 + 2.5x + -9 = 0

Reorder the terms:
-9 + 2.5x + x2 = 0

Solving
-9 + 2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2.5x + x2 = 0 + 9
2.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2.5x + x2 = 9

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 9 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 9 + 1.5625

Combine like terms: 9 + 1.5625 = 10.5625
1.5625 + 2.5x + x2 = 10.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.25 and -3.25.

Subproblem 1
x + 1.25 = 3.25

Simplifying
x + 1.25 = 3.25

Reorder the terms:
1.25 + x = 3.25

Solving
1.25 + x = 3.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.25 + -1.25
x = 3.25 + -1.25

Combine like terms: 3.25 + -1.25 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + 1.25 = -3.25

Simplifying
x + 1.25 = -3.25

Reorder the terms:
1.25 + x = -3.25

Solving
1.25 + x = -3.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.25 + -1.25
x = -3.25 + -1.25

Combine like terms: -3.25 + -1.25 = -4.5
x = -4.5

Simplifying
x = -4.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -4.5}