1080=2x^2+4x-48

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Solution for 1080=2x^2+4x-48 equation: 


Simplifying
1080 = 2x2 + 4x + -48

Reorder the terms:
1080 = -48 + 4x + 2x2

Solving
1080 = -48 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 1080 + 48 = 1128
1128 + -4x + -2x2 = -48 + 4x + 2x2 + 48 + -4x + -2x2

Reorder the terms:
1128 + -4x + -2x2 = -48 + 48 + 4x + -4x + 2x2 + -2x2

Combine like terms: -48 + 48 = 0
1128 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
1128 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
1128 + -4x + -2x2 = 0 + 2x2 + -2x2
1128 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1128 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(564 + -2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(564 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
564 + -2x + -1x2 = 0

Solving
564 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-564 + 2x + x2 = 0

Move the constant term to the right:

Add '564' to each side of the equation.
-564 + 2x + 564 + x2 = 0 + 564

Reorder the terms:
-564 + 564 + 2x + x2 = 0 + 564

Combine like terms: -564 + 564 = 0
0 + 2x + x2 = 0 + 564
2x + x2 = 0 + 564

Combine like terms: 0 + 564 = 564
2x + x2 = 564

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 564 + 1

Reorder the terms:
1 + 2x + x2 = 564 + 1

Combine like terms: 564 + 1 = 565
1 + 2x + x2 = 565

Factor a perfect square on the left side:
(x + 1)(x + 1) = 565

Calculate the square root of the right side: 23.769728648

Break this problem into two subproblems by setting 
(x + 1) equal to 23.769728648 and -23.769728648.


Subproblem 1
x + 1 = 23.769728648

Simplifying
x + 1 = 23.769728648

Reorder the terms:
1 + x = 23.769728648

Solving
1 + x = 23.769728648

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 23.769728648 + -1

Combine like terms: 1 + -1 = 0
0 + x = 23.769728648 + -1
x = 23.769728648 + -1

Combine like terms: 23.769728648 + -1 = 22.769728648
x = 22.769728648

Simplifying
x = 22.769728648


Subproblem 2
x + 1 = -23.769728648

Simplifying
x + 1 = -23.769728648

Reorder the terms:
1 + x = -23.769728648

Solving
1 + x = -23.769728648

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -23.769728648 + -1

Combine like terms: 1 + -1 = 0
0 + x = -23.769728648 + -1
x = -23.769728648 + -1

Combine like terms: -23.769728648 + -1 = -24.769728648
x = -24.769728648

Simplifying
x = -24.769728648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.769728648, -24.769728648}
Solution
x = {22.769728648, -24.769728648}

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