3x^2+10x-30=0

Simple and best practice solution for 3x^2+10x-30=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 3x^2+10x-30=0 equation: 


Simplifying
3x2 + 10x + -30 = 0

Reorder the terms:
-30 + 10x + 3x2 = 0

Solving
-30 + 10x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-10 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 3.333333333x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 3.333333333x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3.333333333x + x2 = 0 + 10
3.333333333x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
3.333333333x + x2 = 10

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 10 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 10 + 2.777777779

Combine like terms: 10 + 2.777777779 = 12.777777779
2.777777779 + 3.333333333x + x2 = 12.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 12.777777779

Calculate the square root of the right side: 3.574601765

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.574601765 and -3.574601765.


Subproblem 1
x + 1.666666667 = 3.574601765

Simplifying
x + 1.666666667 = 3.574601765

Reorder the terms:
1.666666667 + x = 3.574601765

Solving
1.666666667 + x = 3.574601765

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 3.574601765 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 3.574601765 + -1.666666667
x = 3.574601765 + -1.666666667

Combine like terms: 3.574601765 + -1.666666667 = 1.907935098
x = 1.907935098

Simplifying
x = 1.907935098


Subproblem 2
x + 1.666666667 = -3.574601765

Simplifying
x + 1.666666667 = -3.574601765

Reorder the terms:
1.666666667 + x = -3.574601765

Solving
1.666666667 + x = -3.574601765

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -3.574601765 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -3.574601765 + -1.666666667
x = -3.574601765 + -1.666666667

Combine like terms: -3.574601765 + -1.666666667 = -5.241268432
x = -5.241268432

Simplifying
x = -5.241268432


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.907935098, -5.241268432}

See similar equations:

| 4x^2+10x-30=0 | | 2x^2+10x-30=0 | | 8(2x+1)=-4x+48 | | [2d]+3=21 | | -4(9+5)= | | 0=-16t^2+225t | | 9y+7y=112 | | 10x^2+10x-30=0 | | -2x-10y=58 | | 5x+3(2x+11)=44 | | 8c+16-6c=20 | | 2w^2-w-21= | | 6x+5=x-25 | | 6-7y=2(-4)y+1 | | r-15=63 | | -3(3b+1)+(10b-3)=0 | | -90b+100+92b=104 | | -4+3x=23 | | 4(x+5)=300 | | w(3w)=(w+2)(2w) | | -6y+5=-7y+6 | | 4+3x=23 | | (-2+z)+y+z=6 | | 23=4-3x | | 56.9=34+p | | -6(t+2)=12 | | 7x+24=3 | | 8-5x=40 | | y^2-3y-22=0 | | 56.9=34 | | 2.2x+54=3.7x+18 | | y^2-6y-22=0 |

Equations solver categories