x^2-1.5x-8=0

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Solution for x^2-1.5x-8=0 equation: 


Simplifying
x2 + -1.5x + -8 = 0

Reorder the terms:
-8 + -1.5x + x2 = 0

Solving
-8 + -1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -1.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1.5x + x2 = 0 + 8
-1.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1.5x + x2 = 8

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 = 8 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 8 + 0.5625

Combine like terms: 8 + 0.5625 = 8.5625
0.5625 + -1.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.926174978 and -2.926174978.


Subproblem 1
x + -0.75 = 2.926174978

Simplifying
x + -0.75 = 2.926174978

Reorder the terms:
-0.75 + x = 2.926174978

Solving
-0.75 + x = 2.926174978

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 = 2.926174978 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 2.926174978 + 0.75
x = 2.926174978 + 0.75

Combine like terms: 2.926174978 + 0.75 = 3.676174978
x = 3.676174978

Simplifying
x = 3.676174978


Subproblem 2
x + -0.75 = -2.926174978

Simplifying
x + -0.75 = -2.926174978

Reorder the terms:
-0.75 + x = -2.926174978

Solving
-0.75 + x = -2.926174978

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 = -2.926174978 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -2.926174978 + 0.75
x = -2.926174978 + 0.75

Combine like terms: -2.926174978 + 0.75 = -2.176174978
x = -2.176174978

Simplifying
x = -2.176174978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.676174978, -2.176174978}

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