x^2-0.7x=-.10

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Solution for x^2-0.7x=-.10 equation: 


Simplifying
x2 + -0.7x = -0.10

Reorder the terms:
-0.7x + x2 = -0.10

Solving
-0.7x + x2 = -0.10

Solving for variable 'x'.

Reorder the terms:
0.10 + -0.7x + x2 = -0.10 + 0.10

Combine like terms: -0.10 + 0.10 = 0.00
0.10 + -0.7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.10' to each side of the equation.
0.10 + -0.7x + -0.10 + x2 = 0.00 + -0.10

Reorder the terms:
0.10 + -0.10 + -0.7x + x2 = 0.00 + -0.10

Combine like terms: 0.10 + -0.10 = 0.00
0.00 + -0.7x + x2 = 0.00 + -0.10
-0.7x + x2 = 0.00 + -0.10

Combine like terms: 0.00 + -0.10 = -0.1
-0.7x + x2 = -0.1

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = -0.1 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = -0.1 + 0.1225

Combine like terms: -0.1 + 0.1225 = 0.0225
0.1225 + -0.7x + x2 = 0.0225

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + -0.35) equal to 0.15 and -0.15.


Subproblem 1
x + -0.35 = 0.15

Simplifying
x + -0.35 = 0.15

Reorder the terms:
-0.35 + x = 0.15

Solving
-0.35 + x = 0.15

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = 0.15 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = 0.15 + 0.35
x = 0.15 + 0.35

Combine like terms: 0.15 + 0.35 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + -0.35 = -0.15

Simplifying
x + -0.35 = -0.15

Reorder the terms:
-0.35 + x = -0.15

Solving
-0.35 + x = -0.15

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = -0.15 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = -0.15 + 0.35
x = -0.15 + 0.35

Combine like terms: -0.15 + 0.35 = 0.2
x = 0.2

Simplifying
x = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, 0.2}

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