50x^2-11x-24=0

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Solution for 50x^2-11x-24=0 equation: 


Simplifying
50x2 + -11x + -24 = 0

Reorder the terms:
-24 + -11x + 50x2 = 0

Solving
-24 + -11x + 50x2 = 0

Solving for variable 'x'.

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

Divide each side by '50'.
-0.48 + -0.22x + x2 = 0

Move the constant term to the right:

Add '0.48' to each side of the equation.
-0.48 + -0.22x + 0.48 + x2 = 0 + 0.48

Reorder the terms:
-0.48 + 0.48 + -0.22x + x2 = 0 + 0.48

Combine like terms: -0.48 + 0.48 = 0.00
0.00 + -0.22x + x2 = 0 + 0.48
-0.22x + x2 = 0 + 0.48

Combine like terms: 0 + 0.48 = 0.48
-0.22x + x2 = 0.48

The x term is -0.22x.  Take half its coefficient (-0.11).
Square it (0.0121) and add it to both sides.

Add '0.0121' to each side of the equation.
-0.22x + 0.0121 + x2 = 0.48 + 0.0121

Reorder the terms:
0.0121 + -0.22x + x2 = 0.48 + 0.0121

Combine like terms: 0.48 + 0.0121 = 0.4921
0.0121 + -0.22x + x2 = 0.4921

Factor a perfect square on the left side:
(x + -0.11)(x + -0.11) = 0.4921

Calculate the square root of the right side: 0.701498396

Break this problem into two subproblems by setting 
(x + -0.11) equal to 0.701498396 and -0.701498396.


Subproblem 1
x + -0.11 = 0.701498396

Simplifying
x + -0.11 = 0.701498396

Reorder the terms:
-0.11 + x = 0.701498396

Solving
-0.11 + x = 0.701498396

Solving for variable 'x'.

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

Add '0.11' to each side of the equation.
-0.11 + 0.11 + x = 0.701498396 + 0.11

Combine like terms: -0.11 + 0.11 = 0.00
0.00 + x = 0.701498396 + 0.11
x = 0.701498396 + 0.11

Combine like terms: 0.701498396 + 0.11 = 0.811498396
x = 0.811498396

Simplifying
x = 0.811498396


Subproblem 2
x + -0.11 = -0.701498396

Simplifying
x + -0.11 = -0.701498396

Reorder the terms:
-0.11 + x = -0.701498396

Solving
-0.11 + x = -0.701498396

Solving for variable 'x'.

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

Add '0.11' to each side of the equation.
-0.11 + 0.11 + x = -0.701498396 + 0.11

Combine like terms: -0.11 + 0.11 = 0.00
0.00 + x = -0.701498396 + 0.11
x = -0.701498396 + 0.11

Combine like terms: -0.701498396 + 0.11 = -0.591498396
x = -0.591498396

Simplifying
x = -0.591498396


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.811498396, -0.591498396}

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