-1.25=x^2+2.5x-4

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Solution for -1.25=x^2+2.5x-4 equation: 


Simplifying
-1.25 = x2 + 2.5x + -4

Reorder the terms:
-1.25 = -4 + 2.5x + x2

Solving
-1.25 = -4 + 2.5x + x2

Solving for variable 'x'.

Combine like terms: -1.25 + 4 = 2.75
2.75 + -2.5x + -1x2 = -4 + 2.5x + x2 + 4 + -2.5x + -1x2

Reorder the terms:
2.75 + -2.5x + -1x2 = -4 + 4 + 2.5x + -2.5x + x2 + -1x2

Combine like terms: -4 + 4 = 0
2.75 + -2.5x + -1x2 = 0 + 2.5x + -2.5x + x2 + -1x2
2.75 + -2.5x + -1x2 = 2.5x + -2.5x + x2 + -1x2

Combine like terms: 2.5x + -2.5x = 0.0
2.75 + -2.5x + -1x2 = 0.0 + x2 + -1x2
2.75 + -2.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2.75 + -2.5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 2.5x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 2.5x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 2.5x + x2 = 0 + 2.75
2.5x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
2.5x + x2 = 2.75

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 = 2.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 2.75 + 1.5625

Combine like terms: 2.75 + 1.5625 = 4.3125
1.5625 + 2.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
x + 1.25 = 2.076655966

Simplifying
x + 1.25 = 2.076655966

Reorder the terms:
1.25 + x = 2.076655966

Solving
1.25 + x = 2.076655966

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 = 2.076655966 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.076655966 + -1.25
x = 2.076655966 + -1.25

Combine like terms: 2.076655966 + -1.25 = 0.826655966
x = 0.826655966

Simplifying
x = 0.826655966


Subproblem 2
x + 1.25 = -2.076655966

Simplifying
x + 1.25 = -2.076655966

Reorder the terms:
1.25 + x = -2.076655966

Solving
1.25 + x = -2.076655966

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 = -2.076655966 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.076655966 + -1.25
x = -2.076655966 + -1.25

Combine like terms: -2.076655966 + -1.25 = -3.326655966
x = -3.326655966

Simplifying
x = -3.326655966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.826655966, -3.326655966}

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