24x^2-96x-152=0

Simple and best practice solution for 24x^2-96x-152=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 24x^2-96x-152=0 equation: 


Simplifying
24x2 + -96x + -152 = 0

Reorder the terms:
-152 + -96x + 24x2 = 0

Solving
-152 + -96x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-19 + -12x + 3x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-19 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-19 + -12x + 3x2 = 0

Solving
-19 + -12x + 3x2 = 0

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

Divide each side by '3'.
-6.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -4x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -4x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 6.333333333
-4x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-4x + x2 = 6.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 6.333333333 + 4

Reorder the terms:
4 + -4x + x2 = 6.333333333 + 4

Combine like terms: 6.333333333 + 4 = 10.333333333
4 + -4x + x2 = 10.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 10.333333333

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(x + -2) equal to 3.214550254 and -3.214550254.


Subproblem 1
x + -2 = 3.214550254

Simplifying
x + -2 = 3.214550254

Reorder the terms:
-2 + x = 3.214550254

Solving
-2 + x = 3.214550254

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.214550254 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.214550254 + 2
x = 3.214550254 + 2

Combine like terms: 3.214550254 + 2 = 5.214550254
x = 5.214550254

Simplifying
x = 5.214550254


Subproblem 2
x + -2 = -3.214550254

Simplifying
x + -2 = -3.214550254

Reorder the terms:
-2 + x = -3.214550254

Solving
-2 + x = -3.214550254

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.214550254 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.214550254 + 2
x = -3.214550254 + 2

Combine like terms: -3.214550254 + 2 = -1.214550254
x = -1.214550254

Simplifying
x = -1.214550254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.214550254, -1.214550254}
Solution
x = {5.214550254, -1.214550254}

See similar equations:

| N^2+7n+13=0 | | 9(2+-4x)=4(4+-5x) | | 12x-5+65=180 | | 12+7n+12=0 | | 2y+4(y+1)= | | (4x-20)+(x)=180 | | x=50-2y | | x+x+71+x-11=180 | | -31[1-(y+7)]+5=2(4-y) | | r^2-15r+54= | | -378=-7(-8+6) | | 6+2(t-2)=4(3t-14) | | 9(g+34)=441 | | -4x-6y=0 | | 37+6x=-35-42x | | 24n^2-12n=0 | | 3x+x-2=x+7 | | -2(-5x-2)=-2 | | 3c+12=0 | | 2z-14=22 | | 2(a+3)=4a+20 | | 2x+3y-4x=-3 | | -(-4x-3)=-21 | | (x+24)=90 | | -2(4x-3)=-5 | | Y=6E+0.6x+-8826.2 | | 14x-1=5x+5+6 | | 18=13-y | | Y=6E+0.6x-8826.2 | | 3(t+1)=1 | | 60=1+x^35 | | x-23=52 |

Equations solver categories