1.4=0.2x-0.003x^2

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Solution for 1.4=0.2x-0.003x^2 equation: 


Simplifying
1.4 = 0.2x + -0.003x2

Solving
1.4 = 0.2x + -0.003x2

Solving for variable 'x'.

Reorder the terms:
1.4 + -0.2x + 0.003x2 = 0.2x + -0.2x + -0.003x2 + 0.003x2

Combine like terms: 0.2x + -0.2x = 0.0
1.4 + -0.2x + 0.003x2 = 0.0 + -0.003x2 + 0.003x2
1.4 + -0.2x + 0.003x2 = -0.003x2 + 0.003x2

Combine like terms: -0.003x2 + 0.003x2 = 0.000
1.4 + -0.2x + 0.003x2 = 0.000

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

Divide each side by '0.003'.
466.6666667 + -66.66666667x + x2 = 0

Move the constant term to the right:

Add '-466.6666667' to each side of the equation.
466.6666667 + -66.66666667x + -466.6666667 + x2 = 0 + -466.6666667

Reorder the terms:
466.6666667 + -466.6666667 + -66.66666667x + x2 = 0 + -466.6666667

Combine like terms: 466.6666667 + -466.6666667 = 0.0000000
0.0000000 + -66.66666667x + x2 = 0 + -466.6666667
-66.66666667x + x2 = 0 + -466.6666667

Combine like terms: 0 + -466.6666667 = -466.6666667
-66.66666667x + x2 = -466.6666667

The x term is -66.66666667x.  Take half its coefficient (-33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
-66.66666667x + 1111.111112 + x2 = -466.6666667 + 1111.111112

Reorder the terms:
1111.111112 + -66.66666667x + x2 = -466.6666667 + 1111.111112

Combine like terms: -466.6666667 + 1111.111112 = 644.4444453
1111.111112 + -66.66666667x + x2 = 644.4444453

Factor a perfect square on the left side:
(x + -33.33333334)(x + -33.33333334) = 644.4444453

Calculate the square root of the right side: 25.38591037

Break this problem into two subproblems by setting 
(x + -33.33333334) equal to 25.38591037 and -25.38591037.


Subproblem 1
x + -33.33333334 = 25.38591037

Simplifying
x + -33.33333334 = 25.38591037

Reorder the terms:
-33.33333334 + x = 25.38591037

Solving
-33.33333334 + x = 25.38591037

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = 25.38591037 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = 25.38591037 + 33.33333334
x = 25.38591037 + 33.33333334

Combine like terms: 25.38591037 + 33.33333334 = 58.71924371
x = 58.71924371

Simplifying
x = 58.71924371


Subproblem 2
x + -33.33333334 = -25.38591037

Simplifying
x + -33.33333334 = -25.38591037

Reorder the terms:
-33.33333334 + x = -25.38591037

Solving
-33.33333334 + x = -25.38591037

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = -25.38591037 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = -25.38591037 + 33.33333334
x = -25.38591037 + 33.33333334

Combine like terms: -25.38591037 + 33.33333334 = 7.94742297
x = 7.94742297

Simplifying
x = 7.94742297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {58.71924371, 7.94742297}

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