6x^2+57x+90=240

Simple and best practice solution for 6x^2+57x+90=240 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 6x^2+57x+90=240 equation: 


Simplifying
6x2 + 57x + 90 = 240

Reorder the terms:
90 + 57x + 6x2 = 240

Solving
90 + 57x + 6x2 = 240

Solving for variable 'x'.

Reorder the terms:
90 + -240 + 57x + 6x2 = 240 + -240

Combine like terms: 90 + -240 = -150
-150 + 57x + 6x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-150 + 57x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-50 + 19x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-50 + 19x + 2x2)' equal to zero and attempt to solve:

Simplifying
-50 + 19x + 2x2 = 0

Solving
-50 + 19x + 2x2 = 0

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

Divide each side by '2'.
-25 + 9.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 9.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 9.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 9.5x + x2 = 0 + 25
9.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
9.5x + x2 = 25

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 25 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 25 + 22.5625

Combine like terms: 25 + 22.5625 = 47.5625
22.5625 + 9.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + 4.75) equal to 6.896557112 and -6.896557112.


Subproblem 1
x + 4.75 = 6.896557112

Simplifying
x + 4.75 = 6.896557112

Reorder the terms:
4.75 + x = 6.896557112

Solving
4.75 + x = 6.896557112

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 6.896557112 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 6.896557112 + -4.75
x = 6.896557112 + -4.75

Combine like terms: 6.896557112 + -4.75 = 2.146557112
x = 2.146557112

Simplifying
x = 2.146557112


Subproblem 2
x + 4.75 = -6.896557112

Simplifying
x + 4.75 = -6.896557112

Reorder the terms:
4.75 + x = -6.896557112

Solving
4.75 + x = -6.896557112

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -6.896557112 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -6.896557112 + -4.75
x = -6.896557112 + -4.75

Combine like terms: -6.896557112 + -4.75 = -11.646557112
x = -11.646557112

Simplifying
x = -11.646557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.146557112, -11.646557112}
Solution
x = {2.146557112, -11.646557112}

See similar equations:

| x+6(3x+4)=9 | | h=-16t^2+4.5t+6 | | 0.08(y-8)+0.16y=0.04y-0.01(30) | | 5/b=85 | | -1/3=-5/6=u | | 58=4u+14 | | -6n+12=.66(3n-6) | | 6x+5=(2x+1) | | 12=5r-2r+1 | | -x-6(-3x-4)=9 | | 3a-5b=22 | | 4a+2(-3a+2)=16 | | -24=4x-7x+9 | | 0.8b=120 | | n/2/9=-5 | | 2.5x-15=4h | | 2x+1=13.5 | | Y=18X+400 | | -7x+5=1-11x+17 | | -2-4(4x-1)=-94 | | ((t^2)/(t-1)) | | 3/6=5/n-1 | | .006(7-k)+.08(k-4)=1 | | 3x+11=13.5 | | 7x-6-4x=-17 | | -2(1-7p)=110 | | t^2/t-1 | | 8x+5x+2x+2x+x=360 | | -2-4(4x-1)=94 | | -5(7x+7)= | | x^2*5= | | -5n+7n+6-2= |

Equations solver categories