x^2+1.5x-2=0

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


Simplifying
x2 + 1.5x + -2 = 0

Reorder the terms:
-2 + 1.5x + x2 = 0

Solving
-2 + 1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.5x + x2 = 0 + 2
1.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.5x + x2 = 2

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 = 2 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 2 + 0.5625

Combine like terms: 2 + 0.5625 = 2.5625
0.5625 + 1.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + 0.75 = 1.600781059

Simplifying
x + 0.75 = 1.600781059

Reorder the terms:
0.75 + x = 1.600781059

Solving
0.75 + x = 1.600781059

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 = 1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.600781059 + -0.75
x = 1.600781059 + -0.75

Combine like terms: 1.600781059 + -0.75 = 0.850781059
x = 0.850781059

Simplifying
x = 0.850781059


Subproblem 2
x + 0.75 = -1.600781059

Simplifying
x + 0.75 = -1.600781059

Reorder the terms:
0.75 + x = -1.600781059

Solving
0.75 + x = -1.600781059

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 = -1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.600781059 + -0.75
x = -1.600781059 + -0.75

Combine like terms: -1.600781059 + -0.75 = -2.350781059
x = -2.350781059

Simplifying
x = -2.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.850781059, -2.350781059}

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