3x^2+22x-24=0

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Solution for 3x^2+22x-24=0 equation: 


Simplifying
3x2 + 22x + -24 = 0

Reorder the terms:
-24 + 22x + 3x2 = 0

Solving
-24 + 22x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-8 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 7.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 7.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 7.333333333x + x2 = 0 + 8
7.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
7.333333333x + x2 = 8

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 8 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 8 + 13.44444445

Combine like terms: 8 + 13.44444445 = 21.44444445
13.44444445 + 7.333333333x + x2 = 21.44444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 21.44444445

Calculate the square root of the right side: 4.630814664

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 4.630814664 and -4.630814664.


Subproblem 1
x + 3.666666667 = 4.630814664

Simplifying
x + 3.666666667 = 4.630814664

Reorder the terms:
3.666666667 + x = 4.630814664

Solving
3.666666667 + x = 4.630814664

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 4.630814664 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 4.630814664 + -3.666666667
x = 4.630814664 + -3.666666667

Combine like terms: 4.630814664 + -3.666666667 = 0.964147997
x = 0.964147997

Simplifying
x = 0.964147997


Subproblem 2
x + 3.666666667 = -4.630814664

Simplifying
x + 3.666666667 = -4.630814664

Reorder the terms:
3.666666667 + x = -4.630814664

Solving
3.666666667 + x = -4.630814664

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -4.630814664 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -4.630814664 + -3.666666667
x = -4.630814664 + -3.666666667

Combine like terms: -4.630814664 + -3.666666667 = -8.297481331
x = -8.297481331

Simplifying
x = -8.297481331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.964147997, -8.297481331}

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