3x^2+4x=270

Simple and best practice solution for 3x^2+4x=270 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 3x^2+4x=270 equation: 


Simplifying
3x2 + 4x = 270

Reorder the terms:
4x + 3x2 = 270

Solving
4x + 3x2 = 270

Solving for variable 'x'.

Reorder the terms:
-270 + 4x + 3x2 = 270 + -270

Combine like terms: 270 + -270 = 0
-270 + 4x + 3x2 = 0

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

Divide each side by '3'.
-90 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 1.333333333x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 1.333333333x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 1.333333333x + x2 = 0 + 90
1.333333333x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
1.333333333x + x2 = 90

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 90 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 90 + 0.4444444442

Combine like terms: 90 + 0.4444444442 = 90.4444444442
0.4444444442 + 1.333333333x + x2 = 90.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 90.4444444442

Calculate the square root of the right side: 9.510228412

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 9.510228412 and -9.510228412.


Subproblem 1
x + 0.6666666665 = 9.510228412

Simplifying
x + 0.6666666665 = 9.510228412

Reorder the terms:
0.6666666665 + x = 9.510228412

Solving
0.6666666665 + x = 9.510228412

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 9.510228412 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 9.510228412 + -0.6666666665
x = 9.510228412 + -0.6666666665

Combine like terms: 9.510228412 + -0.6666666665 = 8.8435617455
x = 8.8435617455

Simplifying
x = 8.8435617455


Subproblem 2
x + 0.6666666665 = -9.510228412

Simplifying
x + 0.6666666665 = -9.510228412

Reorder the terms:
0.6666666665 + x = -9.510228412

Solving
0.6666666665 + x = -9.510228412

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -9.510228412 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -9.510228412 + -0.6666666665
x = -9.510228412 + -0.6666666665

Combine like terms: -9.510228412 + -0.6666666665 = -10.1768950785
x = -10.1768950785

Simplifying
x = -10.1768950785


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.8435617455, -10.1768950785}

See similar equations:

| 3x+2(4x-4)=14 | | 2(-9-6q)= | | 2(f-7)-8=10 | | 15y-7y=32 | | (5y+4)(7+y)=0 | | 3w-18w=60 | | -2-1x=3x+6 | | 2/1.25 | | x+(3x+12)+30=180 | | 2sin^2x+4sinx+2=0 | | 9n-14=13 | | P/3=5/6 | | 6(12-18c)= | | 0.4y=-64 | | 19+7m=-5(1-2m) | | 6/n=5/6 | | 2=x+1+61.5 | | x*x-2x+4=0 | | 2x+11-5x=13 | | 11=3(b+20)-4 | | x-19=-3x+9 | | x-19=-3x+0 | | 2(4z-3)-3(5z+2)=4(10-z+1) | | 2y+10.8=1.2 | | x+(3x+4)+47=180 | | -2(y-4)=-8 | | 180=85+x+3x+3 | | -2h^2=-72 | | (x^4)+256i=0 | | x-1+6=2 | | 7m^2-11m=0 | | A+(A*0.2)=B |

Equations solver categories