x^2+1.5x-5=0

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Solution for x^2+1.5x-5=0 equation: 


Simplifying
x2 + 1.5x + -5 = 0

Reorder the terms:
-5 + 1.5x + x2 = 0

Solving
-5 + 1.5x + 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 + 1.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 1.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 1.5x + x2 = 0 + 5
1.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
1.5x + x2 = 5

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 = 5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 5 + 0.5625

Combine like terms: 5 + 0.5625 = 5.5625
0.5625 + 1.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.358495283 and -2.358495283.


Subproblem 1
x + 0.75 = 2.358495283

Simplifying
x + 0.75 = 2.358495283

Reorder the terms:
0.75 + x = 2.358495283

Solving
0.75 + x = 2.358495283

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 = 2.358495283 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.358495283 + -0.75
x = 2.358495283 + -0.75

Combine like terms: 2.358495283 + -0.75 = 1.608495283
x = 1.608495283

Simplifying
x = 1.608495283


Subproblem 2
x + 0.75 = -2.358495283

Simplifying
x + 0.75 = -2.358495283

Reorder the terms:
0.75 + x = -2.358495283

Solving
0.75 + x = -2.358495283

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 = -2.358495283 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.358495283 + -0.75
x = -2.358495283 + -0.75

Combine like terms: -2.358495283 + -0.75 = -3.108495283
x = -3.108495283

Simplifying
x = -3.108495283


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.608495283, -3.108495283}

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