10x^2+1.5-8x=0

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Solution for 10x^2+1.5-8x=0 equation: 


Simplifying
10x2 + 1.5 + -8x = 0

Reorder the terms:
1.5 + -8x + 10x2 = 0

Solving
1.5 + -8x + 10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
0.15 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -0.8x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + -0.8x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -0.8x + x2 = 0 + -0.15
-0.8x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
-0.8x + x2 = -0.15

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -0.15 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -0.15 + 0.16

Combine like terms: -0.15 + 0.16 = 0.01
0.16 + -0.8x + x2 = 0.01

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.1 and -0.1.


Subproblem 1
x + -0.4 = 0.1

Simplifying
x + -0.4 = 0.1

Reorder the terms:
-0.4 + x = 0.1

Solving
-0.4 + x = 0.1

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.1 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.1 + 0.4
x = 0.1 + 0.4

Combine like terms: 0.1 + 0.4 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + -0.4 = -0.1

Simplifying
x + -0.4 = -0.1

Reorder the terms:
-0.4 + x = -0.1

Solving
-0.4 + x = -0.1

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.1 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.1 + 0.4
x = -0.1 + 0.4

Combine like terms: -0.1 + 0.4 = 0.3
x = 0.3

Simplifying
x = 0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, 0.3}

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