4x^2-9x-3=0

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Solution for 4x^2-9x-3=0 equation: 


Simplifying
4x2 + -9x + -3 = 0

Reorder the terms:
-3 + -9x + 4x2 = 0

Solving
-3 + -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'.
-0.75 + -2.25x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -2.25x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -2.25x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -2.25x + x2 = 0 + 0.75
-2.25x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-2.25x + x2 = 0.75

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 = 0.75 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 0.75 + 1.265625

Combine like terms: 0.75 + 1.265625 = 2.015625
1.265625 + -2.25x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.419727086 and -1.419727086.


Subproblem 1
x + -1.125 = 1.419727086

Simplifying
x + -1.125 = 1.419727086

Reorder the terms:
-1.125 + x = 1.419727086

Solving
-1.125 + x = 1.419727086

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 = 1.419727086 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.419727086 + 1.125
x = 1.419727086 + 1.125

Combine like terms: 1.419727086 + 1.125 = 2.544727086
x = 2.544727086

Simplifying
x = 2.544727086


Subproblem 2
x + -1.125 = -1.419727086

Simplifying
x + -1.125 = -1.419727086

Reorder the terms:
-1.125 + x = -1.419727086

Solving
-1.125 + x = -1.419727086

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 = -1.419727086 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.419727086 + 1.125
x = -1.419727086 + 1.125

Combine like terms: -1.419727086 + 1.125 = -0.294727086
x = -0.294727086

Simplifying
x = -0.294727086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.544727086, -0.294727086}

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