6x^2+18x-11=0

Simple and best practice solution for 6x^2+18x-11=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 6x^2+18x-11=0 equation:


Simplifying
6x2 + 18x + -11 = 0

Reorder the terms:
-11 + 18x + 6x2 = 0

Solving
-11 + 18x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-1.833333333 + 3x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 3x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 3x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + 1.833333333
3x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
3x + x2 = 1.833333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.833333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.833333333 + 2.25

Combine like terms: 1.833333333 + 2.25 = 4.083333333
2.25 + 3x + x2 = 4.083333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.083333333

Calculate the square root of the right side: 2.020725942

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.020725942 and -2.020725942.

Subproblem 1

x + 1.5 = 2.020725942 Simplifying x + 1.5 = 2.020725942 Reorder the terms: 1.5 + x = 2.020725942 Solving 1.5 + x = 2.020725942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.020725942 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.020725942 + -1.5 x = 2.020725942 + -1.5 Combine like terms: 2.020725942 + -1.5 = 0.520725942 x = 0.520725942 Simplifying x = 0.520725942

Subproblem 2

x + 1.5 = -2.020725942 Simplifying x + 1.5 = -2.020725942 Reorder the terms: 1.5 + x = -2.020725942 Solving 1.5 + x = -2.020725942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.020725942 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.020725942 + -1.5 x = -2.020725942 + -1.5 Combine like terms: -2.020725942 + -1.5 = -3.520725942 x = -3.520725942 Simplifying x = -3.520725942

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.520725942, -3.520725942}

See similar equations:

| 12-p=32 | | 6x+10=x^2+3x | | 2lne^3=4 | | 15+.75+8=45 | | 3.6x=-6.4 | | 45c+10= | | x^2-10x-400=0 | | 5x+3+4x=3(3x-2) | | 6y=4x+36.25 | | x/455=120/100 | | 16+17k^2+4k= | | 39+19b=100 | | 2n=5/25 | | x-(0.1x)=300 | | (3r+5)/2=13 | | 2y+3x=130 | | n^2+25n+66=0 | | 9x-31=12x+11 | | 5/13r=45/32 | | 12-4/5(-5+15)=4 | | 9(x-3)+7=52 | | 1.8c+32=40 | | -10-20x+35x-14=3x+9x | | 10-6x=30-104 | | b^2+6b+72=72 | | -1/2v=-9/10 | | 2/3r=0 | | 25x^2+4(0)=9 | | 3t-4fort=8 | | 1/2m=6t | | ax^2-4a^2x+4a^3=0 | | 6x+4x=50 |

Equations solver categories