48x^2+33x-34=0

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Solution for 48x^2+33x-34=0 equation: 


Simplifying
48x2 + 33x + -34 = 0

Reorder the terms:
-34 + 33x + 48x2 = 0

Solving
-34 + 33x + 48x2 = 0

Solving for variable 'x'.

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

Divide each side by '48'.
-0.7083333333 + 0.6875x + x2 = 0

Move the constant term to the right:

Add '0.7083333333' to each side of the equation.
-0.7083333333 + 0.6875x + 0.7083333333 + x2 = 0 + 0.7083333333

Reorder the terms:
-0.7083333333 + 0.7083333333 + 0.6875x + x2 = 0 + 0.7083333333

Combine like terms: -0.7083333333 + 0.7083333333 = 0.0000000000
0.0000000000 + 0.6875x + x2 = 0 + 0.7083333333
0.6875x + x2 = 0 + 0.7083333333

Combine like terms: 0 + 0.7083333333 = 0.7083333333
0.6875x + x2 = 0.7083333333

The x term is 0.6875x.  Take half its coefficient (0.34375).
Square it (0.1181640625) and add it to both sides.

Add '0.1181640625' to each side of the equation.
0.6875x + 0.1181640625 + x2 = 0.7083333333 + 0.1181640625

Reorder the terms:
0.1181640625 + 0.6875x + x2 = 0.7083333333 + 0.1181640625

Combine like terms: 0.7083333333 + 0.1181640625 = 0.8264973958
0.1181640625 + 0.6875x + x2 = 0.8264973958

Factor a perfect square on the left side:
(x + 0.34375)(x + 0.34375) = 0.8264973958

Calculate the square root of the right side: 0.909119022

Break this problem into two subproblems by setting 
(x + 0.34375) equal to 0.909119022 and -0.909119022.


Subproblem 1
x + 0.34375 = 0.909119022

Simplifying
x + 0.34375 = 0.909119022

Reorder the terms:
0.34375 + x = 0.909119022

Solving
0.34375 + x = 0.909119022

Solving for variable 'x'.

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

Add '-0.34375' to each side of the equation.
0.34375 + -0.34375 + x = 0.909119022 + -0.34375

Combine like terms: 0.34375 + -0.34375 = 0.00000
0.00000 + x = 0.909119022 + -0.34375
x = 0.909119022 + -0.34375

Combine like terms: 0.909119022 + -0.34375 = 0.565369022
x = 0.565369022

Simplifying
x = 0.565369022


Subproblem 2
x + 0.34375 = -0.909119022

Simplifying
x + 0.34375 = -0.909119022

Reorder the terms:
0.34375 + x = -0.909119022

Solving
0.34375 + x = -0.909119022

Solving for variable 'x'.

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

Add '-0.34375' to each side of the equation.
0.34375 + -0.34375 + x = -0.909119022 + -0.34375

Combine like terms: 0.34375 + -0.34375 = 0.00000
0.00000 + x = -0.909119022 + -0.34375
x = -0.909119022 + -0.34375

Combine like terms: -0.909119022 + -0.34375 = -1.252869022
x = -1.252869022

Simplifying
x = -1.252869022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.565369022, -1.252869022}

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