4x^2+6x-162=0

Simple and best practice solution for 4x^2+6x-162=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 4x^2+6x-162=0 equation: 


Simplifying
4x2 + 6x + -162 = 0

Reorder the terms:
-162 + 6x + 4x2 = 0

Solving
-162 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-81 + 3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-81 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-81 + 3x + 2x2 = 0

Solving
-81 + 3x + 2x2 = 0

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

Divide each side by '2'.
-40.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '40.5' to each side of the equation.
-40.5 + 1.5x + 40.5 + x2 = 0 + 40.5

Reorder the terms:
-40.5 + 40.5 + 1.5x + x2 = 0 + 40.5

Combine like terms: -40.5 + 40.5 = 0.0
0.0 + 1.5x + x2 = 0 + 40.5
1.5x + x2 = 0 + 40.5

Combine like terms: 0 + 40.5 = 40.5
1.5x + x2 = 40.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 40.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 40.5 + 0.5625

Combine like terms: 40.5 + 0.5625 = 41.0625
0.5625 + 1.5x + x2 = 41.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 41.0625

Calculate the square root of the right side: 6.408002809

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.408002809 and -6.408002809.


Subproblem 1
x + 0.75 = 6.408002809

Simplifying
x + 0.75 = 6.408002809

Reorder the terms:
0.75 + x = 6.408002809

Solving
0.75 + x = 6.408002809

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 6.408002809 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 6.408002809 + -0.75
x = 6.408002809 + -0.75

Combine like terms: 6.408002809 + -0.75 = 5.658002809
x = 5.658002809

Simplifying
x = 5.658002809


Subproblem 2
x + 0.75 = -6.408002809

Simplifying
x + 0.75 = -6.408002809

Reorder the terms:
0.75 + x = -6.408002809

Solving
0.75 + x = -6.408002809

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -6.408002809 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -6.408002809 + -0.75
x = -6.408002809 + -0.75

Combine like terms: -6.408002809 + -0.75 = -7.158002809
x = -7.158002809

Simplifying
x = -7.158002809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.658002809, -7.158002809}
Solution
x = {5.658002809, -7.158002809}

See similar equations:

| 7x^4+6x^3+-78x^2+-66x+11=0 | | -2+2=-3 | | 19.95-5.5j+3.33=-9.7j-19.98 | | 120-28q=78 | | 409=3(5x+6)+8 | | 20x+15=215 | | 7g-8=16.5 | | X-10x=-16 | | -6.31-15.7q=3.44-15.2q | | RS=7y+3 | | 6d+18=27 | | 8u+7(u-8)=-11 | | 3=2w+15 | | 2y-8=6x | | 7.1z=3.8z-4.29 | | 7m-3=25-3m | | -3t+15=-4-2t | | 36=-7v+2(v+3) | | 2(X+6)+2x=106 | | -4v+2-12v=-17v+19 | | -4x-2+7x=9x+10 | | 4x-5=13x-2 | | (6+x)x(8+x)=120 | | 5y-3y=-6 | | 3x+4=101 | | 15y^3-95y^2-70y=0 | | a(2x-5)=b-18x | | -16-9h=-8h | | -27+-9= | | 5=8x-3 | | 3w+1.2w=w | | 1b=21 |

Equations solver categories