2x^2+24x=40

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Solution for 2x^2+24x=40 equation:


Simplifying
2x2 + 24x = 40

Reorder the terms:
24x + 2x2 = 40

Solving
24x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 24x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 12x + x2 = 0

Solving
-20 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 12x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 12x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 12x + x2 = 0 + 20
12x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
12x + x2 = 20

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 20 + 36

Reorder the terms:
36 + 12x + x2 = 20 + 36

Combine like terms: 20 + 36 = 56
36 + 12x + x2 = 56

Factor a perfect square on the left side:
(x + 6)(x + 6) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 6) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + 6 = 7.483314774

Simplifying
x + 6 = 7.483314774

Reorder the terms:
6 + x = 7.483314774

Solving
6 + x = 7.483314774

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 7.483314774 + -6

Combine like terms: 6 + -6 = 0
0 + x = 7.483314774 + -6
x = 7.483314774 + -6

Combine like terms: 7.483314774 + -6 = 1.483314774
x = 1.483314774

Simplifying
x = 1.483314774


Subproblem 2
x + 6 = -7.483314774

Simplifying
x + 6 = -7.483314774

Reorder the terms:
6 + x = -7.483314774

Solving
6 + x = -7.483314774

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -7.483314774 + -6

Combine like terms: 6 + -6 = 0
0 + x = -7.483314774 + -6
x = -7.483314774 + -6

Combine like terms: -7.483314774 + -6 = -13.483314774
x = -13.483314774

Simplifying
x = -13.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.483314774, -13.483314774}
Solution
x = {1.483314774, -13.483314774}

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