-2.5x^2+5x+37.5=

Solution for -2.5x^2+5x+37.5= equation:

Simplifying
-2.5x2 + 5x + 37.5 = 0

Reorder the terms:
37.5 + 5x + -2.5x2 = 0

Solving
37.5 + 5x + -2.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
-15 + -2x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -2x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -2x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x + x2 = 0 + 15
-2x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-2x + x2 = 15

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 15 + 1

Reorder the terms:
1 + -2x + x2 = 15 + 1

Combine like terms: 15 + 1 = 16
1 + -2x + x2 = 16

Factor a perfect square on the left side:
(x + -1)(x + -1) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -1) equal to 4 and -4.

Subproblem 1
x + -1 = 4

Simplifying
x + -1 = 4

Reorder the terms:
-1 + x = 4

Solving
-1 + x = 4

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4 + 1
x = 4 + 1

Combine like terms: 4 + 1 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + -1 = -4

Simplifying
x + -1 = -4

Reorder the terms:
-1 + x = -4

Solving
-1 + x = -4

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4 + 1
x = -4 + 1

Combine like terms: -4 + 1 = -3
x = -3

Simplifying
x = -3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -3}