x^2+1.25x-5=0

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Solution for x^2+1.25x-5=0 equation: 


Simplifying
x2 + 1.25x + -5 = 0

Reorder the terms:
-5 + 1.25x + x2 = 0

Solving
-5 + 1.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 1.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 1.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 1.25x + x2 = 0 + 5
1.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
1.25x + x2 = 5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 5 + 0.390625

Combine like terms: 5 + 0.390625 = 5.390625
0.390625 + 1.25x + x2 = 5.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 5.390625

Calculate the square root of the right side: 2.321771953

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.321771953 and -2.321771953.


Subproblem 1
x + 0.625 = 2.321771953

Simplifying
x + 0.625 = 2.321771953

Reorder the terms:
0.625 + x = 2.321771953

Solving
0.625 + x = 2.321771953

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 2.321771953 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.321771953 + -0.625
x = 2.321771953 + -0.625

Combine like terms: 2.321771953 + -0.625 = 1.696771953
x = 1.696771953

Simplifying
x = 1.696771953


Subproblem 2
x + 0.625 = -2.321771953

Simplifying
x + 0.625 = -2.321771953

Reorder the terms:
0.625 + x = -2.321771953

Solving
0.625 + x = -2.321771953

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -2.321771953 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.321771953 + -0.625
x = -2.321771953 + -0.625

Combine like terms: -2.321771953 + -0.625 = -2.946771953
x = -2.946771953

Simplifying
x = -2.946771953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.696771953, -2.946771953}

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