0.1x^2+1.6x+1.5=0

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Solution for 0.1x^2+1.6x+1.5=0 equation: 


Simplifying
0.1x2 + 1.6x + 1.5 = 0

Reorder the terms:
1.5 + 1.6x + 0.1x2 = 0

Solving
1.5 + 1.6x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
15 + 16x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 16x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 16x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 16x + x2 = 0 + -15
16x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
16x + x2 = -15

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -15 + 64

Reorder the terms:
64 + 16x + x2 = -15 + 64

Combine like terms: -15 + 64 = 49
64 + 16x + x2 = 49

Factor a perfect square on the left side:
(x + 8)(x + 8) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + 8) equal to 7 and -7.


Subproblem 1
x + 8 = 7

Simplifying
x + 8 = 7

Reorder the terms:
8 + x = 7

Solving
8 + x = 7

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7 + -8
x = 7 + -8

Combine like terms: 7 + -8 = -1
x = -1

Simplifying
x = -1


Subproblem 2
x + 8 = -7

Simplifying
x + 8 = -7

Reorder the terms:
8 + x = -7

Solving
8 + x = -7

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7 + -8
x = -7 + -8

Combine like terms: -7 + -8 = -15
x = -15

Simplifying
x = -15


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -15}

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