0.2x^2+0.1x+0.7=10

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Solution for 0.2x^2+0.1x+0.7=10 equation: 


Simplifying
0.2x2 + 0.1x + 0.7 = 10

Reorder the terms:
0.7 + 0.1x + 0.2x2 = 10

Solving
0.7 + 0.1x + 0.2x2 = 10

Solving for variable 'x'.

Reorder the terms:
0.7 + -10 + 0.1x + 0.2x2 = 10 + -10

Combine like terms: 0.7 + -10 = -9.3
-9.3 + 0.1x + 0.2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9.3 + 0.1x + 0.2x2 = 0

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

Divide each side by '0.2'.
-46.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '46.5' to each side of the equation.
-46.5 + 0.5x + 46.5 + x2 = 0 + 46.5

Reorder the terms:
-46.5 + 46.5 + 0.5x + x2 = 0 + 46.5

Combine like terms: -46.5 + 46.5 = 0.0
0.0 + 0.5x + x2 = 0 + 46.5
0.5x + x2 = 0 + 46.5

Combine like terms: 0 + 46.5 = 46.5
0.5x + x2 = 46.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 46.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 46.5 + 0.0625

Combine like terms: 46.5 + 0.0625 = 46.5625
0.0625 + 0.5x + x2 = 46.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 46.5625

Calculate the square root of the right side: 6.823672032

Break this problem into two subproblems by setting 
(x + 0.25) equal to 6.823672032 and -6.823672032.


Subproblem 1
x + 0.25 = 6.823672032

Simplifying
x + 0.25 = 6.823672032

Reorder the terms:
0.25 + x = 6.823672032

Solving
0.25 + x = 6.823672032

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 6.823672032 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 6.823672032 + -0.25
x = 6.823672032 + -0.25

Combine like terms: 6.823672032 + -0.25 = 6.573672032
x = 6.573672032

Simplifying
x = 6.573672032


Subproblem 2
x + 0.25 = -6.823672032

Simplifying
x + 0.25 = -6.823672032

Reorder the terms:
0.25 + x = -6.823672032

Solving
0.25 + x = -6.823672032

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -6.823672032 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -6.823672032 + -0.25
x = -6.823672032 + -0.25

Combine like terms: -6.823672032 + -0.25 = -7.073672032
x = -7.073672032

Simplifying
x = -7.073672032


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.573672032, -7.073672032}

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