x^2+1.5*x-0.25=0

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Solution for x^2+1.5*x-0.25=0 equation: 


Simplifying
x2 + 1.5x + -0.25 = 0

Reorder the terms:
-0.25 + 1.5x + x2 = 0

Solving
-0.25 + 1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.5x + x2 = 0 + 0.25
1.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.5x + x2 = 0.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + 1.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.901387819 and -0.901387819.


Subproblem 1
x + 0.75 = 0.901387819

Simplifying
x + 0.75 = 0.901387819

Reorder the terms:
0.75 + x = 0.901387819

Solving
0.75 + x = 0.901387819

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 0.901387819 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.901387819 + -0.75
x = 0.901387819 + -0.75

Combine like terms: 0.901387819 + -0.75 = 0.151387819
x = 0.151387819

Simplifying
x = 0.151387819


Subproblem 2
x + 0.75 = -0.901387819

Simplifying
x + 0.75 = -0.901387819

Reorder the terms:
0.75 + x = -0.901387819

Solving
0.75 + x = -0.901387819

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -0.901387819 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.901387819 + -0.75
x = -0.901387819 + -0.75

Combine like terms: -0.901387819 + -0.75 = -1.651387819
x = -1.651387819

Simplifying
x = -1.651387819


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.151387819, -1.651387819}

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