3x^2+7x-24=0

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Solution for 3x^2+7x-24=0 equation: 


Simplifying
3x2 + 7x + -24 = 0

Reorder the terms:
-24 + 7x + 3x2 = 0

Solving
-24 + 7x + 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 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 2.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 2.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2.333333333x + x2 = 0 + 8
2.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2.333333333x + x2 = 8

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 8 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 8 + 1.361111112

Combine like terms: 8 + 1.361111112 = 9.361111112
1.361111112 + 2.333333333x + x2 = 9.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 9.361111112

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 3.059593292 and -3.059593292.


Subproblem 1
x + 1.166666667 = 3.059593292

Simplifying
x + 1.166666667 = 3.059593292

Reorder the terms:
1.166666667 + x = 3.059593292

Solving
1.166666667 + x = 3.059593292

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 3.059593292 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 3.059593292 + -1.166666667
x = 3.059593292 + -1.166666667

Combine like terms: 3.059593292 + -1.166666667 = 1.892926625
x = 1.892926625

Simplifying
x = 1.892926625


Subproblem 2
x + 1.166666667 = -3.059593292

Simplifying
x + 1.166666667 = -3.059593292

Reorder the terms:
1.166666667 + x = -3.059593292

Solving
1.166666667 + x = -3.059593292

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -3.059593292 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -3.059593292 + -1.166666667
x = -3.059593292 + -1.166666667

Combine like terms: -3.059593292 + -1.166666667 = -4.226259959
x = -4.226259959

Simplifying
x = -4.226259959


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.892926625, -4.226259959}

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