24x^2-4x-27=0

Simple and best practice solution for 24x^2-4x-27=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^2-4x-27=0 equation: 


Simplifying
24x2 + -4x + -27 = 0

Reorder the terms:
-27 + -4x + 24x2 = 0

Solving
-27 + -4x + 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'.
-1.125 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.1666666667x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.1666666667x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.1666666667x + x2 = 0 + 1.125
-0.1666666667x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.1666666667x + x2 = 1.125

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 1.125 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 1.125 + 0.006944444447

Combine like terms: 1.125 + 0.006944444447 = 1.131944444447
0.006944444447 + -0.1666666667x + x2 = 1.131944444447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 1.131944444447

Calculate the square root of the right side: 1.063928778

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 1.063928778 and -1.063928778.


Subproblem 1
x + -0.08333333335 = 1.063928778

Simplifying
x + -0.08333333335 = 1.063928778

Reorder the terms:
-0.08333333335 + x = 1.063928778

Solving
-0.08333333335 + x = 1.063928778

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 1.063928778 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 1.063928778 + 0.08333333335
x = 1.063928778 + 0.08333333335

Combine like terms: 1.063928778 + 0.08333333335 = 1.14726211135
x = 1.14726211135

Simplifying
x = 1.14726211135


Subproblem 2
x + -0.08333333335 = -1.063928778

Simplifying
x + -0.08333333335 = -1.063928778

Reorder the terms:
-0.08333333335 + x = -1.063928778

Solving
-0.08333333335 + x = -1.063928778

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -1.063928778 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -1.063928778 + 0.08333333335
x = -1.063928778 + 0.08333333335

Combine like terms: -1.063928778 + 0.08333333335 = -0.98059544465
x = -0.98059544465

Simplifying
x = -0.98059544465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.14726211135, -0.98059544465}

See similar equations:

| 0=ln(x+6) | | 9z+9-4z=45-4z | | ln(4x+2)=ln(8)+ln(x) | | y+3x+3=180 | | .25y+.40x=10 | | 3(x+3)-5=22 | | 4(x-6)=3(x-8)+x | | 5(X-3310*3)=2850 | | .40x+.25y=10 | | 7y+3(1-y)-y=-6 | | 7y-3(1-y)-y=-6 | | s(5)=25 | | 34-17=x-4 | | (3x+1)(8+x)=0 | | (19b-5)-6(3b+1)=-6 | | 15-5x=-7x+17 | | x-5x+5x-25=0 | | 3(2x-5)=(x-4)+5 | | X-1/14=9/14 | | 0.8x+4.5=1.7 | | 3(2x-5)=(x-4) | | 7+12lnx=4 | | -49+m=14 | | 9x+4x+2+5=5x+3+7x | | 6x^2-54x+84= | | x^4-8x^3+55x^2+138x+74= | | 24-8+15=x-8 | | X-24=-52 | | 1.6+x-3.2=-3+5.7 | | 6=42+-1y-2y | | 5(7x+1)-11=x-(x+5) | | 3-x+2y=9 |

Equations solver categories