-16x^2+48x+50=0

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Solution for -16x^2+48x+50=0 equation: 


Simplifying
-16x2 + 48x + 50 = 0

Reorder the terms:
50 + 48x + -16x2 = 0

Solving
50 + 48x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 24x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 24x + -8x2)' equal to zero and attempt to solve:

Simplifying
25 + 24x + -8x2 = 0

Solving
25 + 24x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-3.125 + -3x + x2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -3x + 3.125 + x2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -3x + x2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -3x + x2 = 0 + 3.125
-3x + x2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-3x + x2 = 3.125

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3.125 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.125 + 2.25

Combine like terms: 3.125 + 2.25 = 5.375
2.25 + -3x + x2 = 5.375

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.375

Calculate the square root of the right side: 2.318404624

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.318404624 and -2.318404624.


Subproblem 1
x + -1.5 = 2.318404624

Simplifying
x + -1.5 = 2.318404624

Reorder the terms:
-1.5 + x = 2.318404624

Solving
-1.5 + x = 2.318404624

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.318404624 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.318404624 + 1.5
x = 2.318404624 + 1.5

Combine like terms: 2.318404624 + 1.5 = 3.818404624
x = 3.818404624

Simplifying
x = 3.818404624


Subproblem 2
x + -1.5 = -2.318404624

Simplifying
x + -1.5 = -2.318404624

Reorder the terms:
-1.5 + x = -2.318404624

Solving
-1.5 + x = -2.318404624

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.318404624 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.318404624 + 1.5
x = -2.318404624 + 1.5

Combine like terms: -2.318404624 + 1.5 = -0.818404624
x = -0.818404624

Simplifying
x = -0.818404624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.818404624, -0.818404624}
Solution
x = {3.818404624, -0.818404624}

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