4x^2+9x-2=0

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


Simplifying
4x2 + 9x + -2 = 0

Reorder the terms:
-2 + 9x + 4x2 = 0

Solving
-2 + 9x + 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'.
-0.5 + 2.25x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.25x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.25x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.25x + x2 = 0 + 0.5
2.25x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.25x + x2 = 0.5

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 0.5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 0.5 + 1.265625

Combine like terms: 0.5 + 1.265625 = 1.765625
1.265625 + 2.25x + x2 = 1.765625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.328768227 and -1.328768227.


Subproblem 1
x + 1.125 = 1.328768227

Simplifying
x + 1.125 = 1.328768227

Reorder the terms:
1.125 + x = 1.328768227

Solving
1.125 + x = 1.328768227

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.328768227 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.328768227 + -1.125
x = 1.328768227 + -1.125

Combine like terms: 1.328768227 + -1.125 = 0.203768227
x = 0.203768227

Simplifying
x = 0.203768227


Subproblem 2
x + 1.125 = -1.328768227

Simplifying
x + 1.125 = -1.328768227

Reorder the terms:
1.125 + x = -1.328768227

Solving
1.125 + x = -1.328768227

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.328768227 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.328768227 + -1.125
x = -1.328768227 + -1.125

Combine like terms: -1.328768227 + -1.125 = -2.453768227
x = -2.453768227

Simplifying
x = -2.453768227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.203768227, -2.453768227}

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