6x^2+25x-24=0

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Solution for 6x^2+25x-24=0 equation: 


Simplifying
6x2 + 25x + -24 = 0

Reorder the terms:
-24 + 25x + 6x2 = 0

Solving
-24 + 25x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-4 + 4.166666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.166666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 4.166666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.166666667x + x2 = 0 + 4
4.166666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
4.166666667x + x2 = 4

The x term is 4.166666667x.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667x + 4.340277781 + x2 = 4 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667x + x2 = 4 + 4.340277781

Combine like terms: 4 + 4.340277781 = 8.340277781
4.340277781 + 4.166666667x + x2 = 8.340277781

Factor a perfect square on the left side:
(x + 2.083333334)(x + 2.083333334) = 8.340277781

Calculate the square root of the right side: 2.887953909

Break this problem into two subproblems by setting 
(x + 2.083333334) equal to 2.887953909 and -2.887953909.


Subproblem 1
x + 2.083333334 = 2.887953909

Simplifying
x + 2.083333334 = 2.887953909

Reorder the terms:
2.083333334 + x = 2.887953909

Solving
2.083333334 + x = 2.887953909

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = 2.887953909 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = 2.887953909 + -2.083333334
x = 2.887953909 + -2.083333334

Combine like terms: 2.887953909 + -2.083333334 = 0.804620575
x = 0.804620575

Simplifying
x = 0.804620575


Subproblem 2
x + 2.083333334 = -2.887953909

Simplifying
x + 2.083333334 = -2.887953909

Reorder the terms:
2.083333334 + x = -2.887953909

Solving
2.083333334 + x = -2.887953909

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = -2.887953909 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = -2.887953909 + -2.083333334
x = -2.887953909 + -2.083333334

Combine like terms: -2.887953909 + -2.083333334 = -4.971287243
x = -4.971287243

Simplifying
x = -4.971287243


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.804620575, -4.971287243}

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