24x^2+30x-88=0

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Solution for 24x^2+30x-88=0 equation: 


Simplifying
24x2 + 30x + -88 = 0

Reorder the terms:
-88 + 30x + 24x2 = 0

Solving
-88 + 30x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 15x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-44 + 15x + 12x2)' equal to zero and attempt to solve:

Simplifying
-44 + 15x + 12x2 = 0

Solving
-44 + 15x + 12x2 = 0

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

Divide each side by '12'.
-3.666666667 + 1.25x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 1.25x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 1.25x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 1.25x + x2 = 0 + 3.666666667
1.25x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
1.25x + x2 = 3.666666667

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 3.666666667 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 3.666666667 + 0.390625

Combine like terms: 3.666666667 + 0.390625 = 4.057291667
0.390625 + 1.25x + x2 = 4.057291667

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 4.057291667

Calculate the square root of the right side: 2.014271994

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.014271994 and -2.014271994.


Subproblem 1
x + 0.625 = 2.014271994

Simplifying
x + 0.625 = 2.014271994

Reorder the terms:
0.625 + x = 2.014271994

Solving
0.625 + x = 2.014271994

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 2.014271994 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.014271994 + -0.625
x = 2.014271994 + -0.625

Combine like terms: 2.014271994 + -0.625 = 1.389271994
x = 1.389271994

Simplifying
x = 1.389271994


Subproblem 2
x + 0.625 = -2.014271994

Simplifying
x + 0.625 = -2.014271994

Reorder the terms:
0.625 + x = -2.014271994

Solving
0.625 + x = -2.014271994

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -2.014271994 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.014271994 + -0.625
x = -2.014271994 + -0.625

Combine like terms: -2.014271994 + -0.625 = -2.639271994
x = -2.639271994

Simplifying
x = -2.639271994


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.389271994, -2.639271994}
Solution
x = {1.389271994, -2.639271994}

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