24x^2-82x-63=0

Simple and best practice solution for 24x^2-82x-63=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^2-82x-63=0 equation: 


Simplifying
24x2 + -82x + -63 = 0

Reorder the terms:
-63 + -82x + 24x2 = 0

Solving
-63 + -82x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
-2.625 + -3.416666667x + x2 = 0

Move the constant term to the right:

Add '2.625' to each side of the equation.
-2.625 + -3.416666667x + 2.625 + x2 = 0 + 2.625

Reorder the terms:
-2.625 + 2.625 + -3.416666667x + x2 = 0 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + -3.416666667x + x2 = 0 + 2.625
-3.416666667x + x2 = 0 + 2.625

Combine like terms: 0 + 2.625 = 2.625
-3.416666667x + x2 = 2.625

The x term is -3.416666667x.  Take half its coefficient (-1.708333334).
Square it (2.918402780) and add it to both sides.

Add '2.918402780' to each side of the equation.
-3.416666667x + 2.918402780 + x2 = 2.625 + 2.918402780

Reorder the terms:
2.918402780 + -3.416666667x + x2 = 2.625 + 2.918402780

Combine like terms: 2.625 + 2.918402780 = 5.54340278
2.918402780 + -3.416666667x + x2 = 5.54340278

Factor a perfect square on the left side:
(x + -1.708333334)(x + -1.708333334) = 5.54340278

Calculate the square root of the right side: 2.3544432

Break this problem into two subproblems by setting 
(x + -1.708333334) equal to 2.3544432 and -2.3544432.


Subproblem 1
x + -1.708333334 = 2.3544432

Simplifying
x + -1.708333334 = 2.3544432

Reorder the terms:
-1.708333334 + x = 2.3544432

Solving
-1.708333334 + x = 2.3544432

Solving for variable 'x'.

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

Add '1.708333334' to each side of the equation.
-1.708333334 + 1.708333334 + x = 2.3544432 + 1.708333334

Combine like terms: -1.708333334 + 1.708333334 = 0.000000000
0.000000000 + x = 2.3544432 + 1.708333334
x = 2.3544432 + 1.708333334

Combine like terms: 2.3544432 + 1.708333334 = 4.062776534
x = 4.062776534

Simplifying
x = 4.062776534


Subproblem 2
x + -1.708333334 = -2.3544432

Simplifying
x + -1.708333334 = -2.3544432

Reorder the terms:
-1.708333334 + x = -2.3544432

Solving
-1.708333334 + x = -2.3544432

Solving for variable 'x'.

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

Add '1.708333334' to each side of the equation.
-1.708333334 + 1.708333334 + x = -2.3544432 + 1.708333334

Combine like terms: -1.708333334 + 1.708333334 = 0.000000000
0.000000000 + x = -2.3544432 + 1.708333334
x = -2.3544432 + 1.708333334

Combine like terms: -2.3544432 + 1.708333334 = -0.646109866
x = -0.646109866

Simplifying
x = -0.646109866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.062776534, -0.646109866}

See similar equations:

| x^2-11xy+24y^2= | | f(75)=0.81x+168.3 | | f(-2)=-2-9 | | 5z+10=6z-6 | | 4z+16=6z-6 | | 4y+5=-1 | | 4z+16=5z+10 | | 4y+5=1 | | x-(2x-5)=3x-8 | | w+8=2w-1 | | 1.5x+1=4x | | 9x+9=10x-1 | | 3b^2-18b=-14 | | 4a^2-4a+4=3 | | -3=-33+5x | | 8x^2+9x=2 | | -3d-5-5d=-3 | | 5a-8=-12 | | x-2Y=-8 | | x-0.30x=13.30 | | 12b+5-7b=25 | | 11x+4y=-24 | | 284+x=354 | | 284+x=413 | | 10-3(2(2)-1)=1 | | V^3=64 | | 2x^4-9x^3-4x^2+27x+20=0 | | y^2-4y-32=0 | | x^2-2+2x=6x-2 | | 42.71+x=51 | | 3n-50=7n+80 | | ln(5)+ln(x)=1 |

Equations solver categories