24x^2+42x-18=0

Simple and best practice solution for 24x^2+42x-18=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+42x-18=0 equation: 


Simplifying
24x2 + 42x + -18 = 0

Reorder the terms:
-18 + 42x + 24x2 = 0

Solving
-18 + 42x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 7x + 4x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-3 + 7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-3 + 7x + 4x2 = 0

Solving
-3 + 7x + 4x2 = 0

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

Divide each side by '4'.
-0.75 + 1.75x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.75x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.75x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.75x + x2 = 0 + 0.75
1.75x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.75x + x2 = 0.75

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 0.75 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 0.75 + 0.765625

Combine like terms: 0.75 + 0.765625 = 1.515625
0.765625 + 1.75x + x2 = 1.515625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.231107225 and -1.231107225.


Subproblem 1
x + 0.875 = 1.231107225

Simplifying
x + 0.875 = 1.231107225

Reorder the terms:
0.875 + x = 1.231107225

Solving
0.875 + x = 1.231107225

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 1.231107225 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 1.231107225 + -0.875
x = 1.231107225 + -0.875

Combine like terms: 1.231107225 + -0.875 = 0.356107225
x = 0.356107225

Simplifying
x = 0.356107225


Subproblem 2
x + 0.875 = -1.231107225

Simplifying
x + 0.875 = -1.231107225

Reorder the terms:
0.875 + x = -1.231107225

Solving
0.875 + x = -1.231107225

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -1.231107225 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -1.231107225 + -0.875
x = -1.231107225 + -0.875

Combine like terms: -1.231107225 + -0.875 = -2.106107225
x = -2.106107225

Simplifying
x = -2.106107225


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.356107225, -2.106107225}
Solution
x = {0.356107225, -2.106107225}

See similar equations:

| 4y^3+108= | | 4x-25=x+3 | | 5x-44=24 | | 5y-12=32 | | 3*x=1 | | 65-2x=9-9x | | 2.6x-17.2=4.2 | | (3y^2+4xy)dx+(4xy+x^2)dy=0 | | v/9.6=6 | | -4x^3y^2= | | 4x+25=x+3 | | 5=6y+4 | | z^2-5z-14/z-7= | | 25.6=2w | | 3cot^2-1=0 | | 2w^2+8w=280 | | -14x-17=-101 | | -4=-2x+2+0.5x | | 6a+7=34-3a | | 9+3n=39 | | T=5x+2y | | 10n+5=10 | | -2(9x+1)+1= | | 10n+9=18 | | 5x-4(3+2x)=9 | | -(-2)x-(-2)x-(-2)= | | 24X=1.9 | | Xy-5y=7 | | e^4x=19 | | -26=-8-6+4x | | -4=0.1x-0.1 | | 8x^2+16-90=0 |

Equations solver categories