4x^2+0.2x-9=0

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Solution for 4x^2+0.2x-9=0 equation: 


Simplifying
4x2 + 0.2x + -9 = 0

Reorder the terms:
-9 + 0.2x + 4x2 = 0

Solving
-9 + 0.2x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2.25 + 0.05x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.05x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.05x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.05x + x2 = 0 + 2.25
0.05x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.05x + x2 = 2.25

The x term is 0.05x.  Take half its coefficient (0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
0.05x + 0.000625 + x2 = 2.25 + 0.000625

Reorder the terms:
0.000625 + 0.05x + x2 = 2.25 + 0.000625

Combine like terms: 2.25 + 0.000625 = 2.250625
0.000625 + 0.05x + x2 = 2.250625

Factor a perfect square on the left side:
(x + 0.025)(x + 0.025) = 2.250625

Calculate the square root of the right side: 1.500208319

Break this problem into two subproblems by setting 
(x + 0.025) equal to 1.500208319 and -1.500208319.


Subproblem 1
x + 0.025 = 1.500208319

Simplifying
x + 0.025 = 1.500208319

Reorder the terms:
0.025 + x = 1.500208319

Solving
0.025 + x = 1.500208319

Solving for variable 'x'.

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

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = 1.500208319 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = 1.500208319 + -0.025
x = 1.500208319 + -0.025

Combine like terms: 1.500208319 + -0.025 = 1.475208319
x = 1.475208319

Simplifying
x = 1.475208319


Subproblem 2
x + 0.025 = -1.500208319

Simplifying
x + 0.025 = -1.500208319

Reorder the terms:
0.025 + x = -1.500208319

Solving
0.025 + x = -1.500208319

Solving for variable 'x'.

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

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = -1.500208319 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = -1.500208319 + -0.025
x = -1.500208319 + -0.025

Combine like terms: -1.500208319 + -0.025 = -1.525208319
x = -1.525208319

Simplifying
x = -1.525208319


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.475208319, -1.525208319}

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