0=4x^2+24x-40

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Solution for 0=4x^2+24x-40 equation: 


Simplifying
0 = 4x2 + 24x + -40

Reorder the terms:
0 = -40 + 24x + 4x2

Solving
0 = -40 + 24x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 40 = 40
40 + -24x + -4x2 = -40 + 24x + 4x2 + 40 + -24x + -4x2

Reorder the terms:
40 + -24x + -4x2 = -40 + 40 + 24x + -24x + 4x2 + -4x2

Combine like terms: -40 + 40 = 0
40 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2
40 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
40 + -24x + -4x2 = 0 + 4x2 + -4x2
40 + -24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
40 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -6x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(10 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -6x + -1x2 = 0

Solving
10 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-10 + 6x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 6x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6x + x2 = 0 + 10
6x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
6x + x2 = 10

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 10 + 9

Reorder the terms:
9 + 6x + x2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + 6x + x2 = 19

Factor a perfect square on the left side:
(x + 3)(x + 3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 3) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + 3 = 4.358898944

Simplifying
x + 3 = 4.358898944

Reorder the terms:
3 + x = 4.358898944

Solving
3 + x = 4.358898944

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + x = 4.358898944 + -3
x = 4.358898944 + -3

Combine like terms: 4.358898944 + -3 = 1.358898944
x = 1.358898944

Simplifying
x = 1.358898944


Subproblem 2
x + 3 = -4.358898944

Simplifying
x + 3 = -4.358898944

Reorder the terms:
3 + x = -4.358898944

Solving
3 + x = -4.358898944

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + x = -4.358898944 + -3
x = -4.358898944 + -3

Combine like terms: -4.358898944 + -3 = -7.358898944
x = -7.358898944

Simplifying
x = -7.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.358898944, -7.358898944}
Solution
x = {1.358898944, -7.358898944}

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